Lunch at the Lab

Lunch at the Lab is a weekly lunchtime gathering of members of the Laboratory and anyone else interested. We meet in the Laboratory on Tuesday between 12.00 and 13.00pm (MS431) for a brown-bag lunch and an informal seminar and discussion. If you would like to be added to our email list for Lunch at the Lab' announcements or other upcoming activities, just ask.

This web-page is maintained by A. Swishchuk. (Last updated: December 12, 2012)

Fall 2012

-->December 11-->

2) Qiu, Chao
(Department of Mathematics & Statistics, U of C): Option Pricing and Hedging under Discrete Time Regime Switching Models'

Abstract: This talk is to explore the option pricing and hedging in a discrete time regime-switching environment. If the regime risk cannot be hedged away, then the Black-Scholes pricing and hedging framework
no longer generates a unique pricing and hedging measure. We also compared several measures for pricing and hedging, with a focus on the risk neutral measure generated by applying Esscher Transforms
to the real world regime-switching asset process. I will also briefly present other works in my research.

-->November 30-->
BP University: Opportunity to learn, network and experience a day as an Energy Trader, Energy Market Analyst and Marketer; BP Centre, 240-4th Ave SW, Calgary, AB, Canada

-->November 27-->
1) Announcement about the BP University: Career Fair Event on November 30

2)  Ware, Antony (Department of Mathematics & Statistics, U of C):  'Splitting Methods in Computational Finance'

-->October 30-->
1)

3) Leonhardt, Daniel (U of C & TUM, Munich, Germany): 'Modeling Multidimensional Futures Prices in a Cointegrated Geometric Model'

Presentation is here

-->September 25-->
Swishchuk, Anatoliy (U of C) & Salvi, Giovanni (Intern. Ph.D. student, U of Rome 'La Sapienza', Rome, Italy): '
Covariance and Correlation Swaps for Markov-modulated Volatility'

-->September 11-->
Hiller, Martin
(Intern. MSc student, TUM, Munich, Germany) & Swishchuk, Anatoliy (U of C) : 'Option pricing in a Black-76 framework with semi-Markov modulated volatility'

Summer 2012

-->August 3--> Pinsky, Ross
(Technion-Israel Institute of Technology, Haifa, Israel):
'Asymptotics for Exit Problem and Principal Eigenvalue for a Class of Non-local Elliptic Operators Related to Diffusion Processes with Jumps'
Abstract
Talk

Spring 2012

-->May 17-->Limnios, Nikolaos (Laboratory of Applied Mathematics, University of Technology Compiegne, Compiegne, France): This talk introduces discrete-time semi-Markov random evolutions (DTSMRE) and studies asymptotic properties, namely, averaging, diffusion approximation and
diffusion approximation with equilibrium by martingale weak convergence method. The applications are given to the additive functionals (AF), geometric Markov renewal processes
(GMRP) and dynamical systems in discrete-time. The rates of convergence in the limit theorems for DTSMRE and AF and GMRP are also presented.

Winter 2012
This Winter 2012 we'll continue, in particular, to do math finance grad students research presentations.

The presentations are below:

1. Ke Zhao:

All presentations are here:

-->April 5-->Shahmoradi, Akbar (MS431, Department of Mathematics & Statistics, U of C): 'US North East and Ontario Power'

-->March 29-->Negahdary, Elham (MS431, Department of Mathematics & Statistics, U of C): 'Taxonomy of Power Models'
Abstract:
This presentation focus on identifying, classifying and characterizing the diversity of trends in electricity market modeling. The pure price processes entail substantial difficulties when are used to model the
evolution of power prices and fail to address the unique features of electricity market such as instantaneous balance of supply and demand.  In this survey of the most recent publications regarding power modeling,
the objective, advantage and disadvantage of each approach is evaluated in context of its application. Finally, the most suitable approaches are identified to answer the question of what causes the price to move.
That “best practice” market-data aware model allows us to capture the evolution of the most salient, primary variables that describe the movement of price.

-->March 22-->Swishchuk, Anatoliy (MS431, Department of Mathematics & Statistics, U of C): 'Stochastic Processes with Independent Increments: Ideas, Results, History'
Abstract:
We give an overview on stochastic processes with independent increments that are now becoming a very popular models in energy and related markets, such as electricity, natural gas, temperature markets, etc.
These processes are more general than Levy processes in a way that the increments are independent, but not necessary stationary. We also present a short history of these processes.

-->March 15-->Salvi, Giovanni, MS431 (Intern. Visiting PhD Student, University of Rome 'La Sapienza', Rome, Italy): 'Backward Time Multivariate semi-Markov Process for Couterparty Credit Risk'

Abstract: We start from the work of Ching et al. on the multivariate Markov chain and we generalize it by allowing any kind of sojourn time distribution, or in other term we introduce a multivariate semi- Markov process.
We derive an explicit expression for the transition probability of this multivariate semi-Markov process in the discrete time case. We apply this multivariate model to the study of the counterparty credit risk, with regard to
correlation in a CDS contract. The financial crisis has stressed the importance of the study of the correlation in the financial market. In this regard, the study of the risk of default of the counterparty in any financial contract
has be- come crucial in the credit risk. Many works has been done to trying to describe the counterparty risk in a CDS contract (see for example Crépey et al.), but all this work are based on the Markovian approach to risk.
In the our opinion this kind of model are too restrictive, because they require that the distribution function of the waiting times has to be exponential or geometric, for discrete time. In the our model, we describe the evolution
of credit rating of the financial subjects like a multivariate semi-Markov model, so we allow for arbitrarily distributed sojourn time. The age state dependency, typical of the semi-Markov environment, allow us to insert the
correlation in a dynamical way. In particular, suppose that A is a default-free bondholder and C is the relative firm. The bondholder buy protection against C’s default by another defaultable subject, say B the protection seller.
Our model describe the evolution of the credit rating of the couple B and C. We admit for simultaneous default of C and B, the single default of C or single default of B.

-->March 8-->Cui, Kaijie (MS431, Department of Mathematics & Statistics, U of C): 'Weather Derivatives with Applications to Canadian Data
ABSTRACT: Modelling of Daily average temperature variations of Canadian Data by a mean-reverting Ornstein-Uhlenbeck process driven by general Levy Process is proposed. The process also contains
seasonal mean and volatility. It is empirically proved that the proposed dynamics fit Calgary and Toronto temperature data successfully. The model is also applied to derive an explicit price of CAT futures,
and numerical prices of CDD and HDD futures using fast Fourier transform are also included.

-->March 1-->Zhang, LiFeng (MS431, Department of Mathematics & Statistics, U of C): 'Geometric Markov Renewal Processes and Their Applications in Finance'
ABSTRACT: First we give some basic concepts and properties on Markov and Semi-Markov Processes and Chains, along with Wiener process and Levy process, all of which are prepared for the next Generalized Geometric Markov Renewal Processes. Next, we introduce Cox-Ross-Rubinstein binomial model and Aase model, and from these cases, generalized GMRP models. Then, we consider its approximation in the geometric Markov renewal processes as model for a security market and also study the processes in a diffusion approximation and normal deviation schemes. As an application, we consider the case of two ergodic classes. We present European call option pricing formulas in the case of ergodic, double-averaged, and merged diffusion geometric Markov renewal processes. Finally, we introduce Poisson averaging scheme for the geometric Markov renewal processes obtain compound Poisson process with deterministic drift and derive its option price under risk-neutral measure. European call option pricing formulas for GMRP are presented.

-->February 16-->Seck, Babacar (MS431, Department of Mathematics & Statistics, U of C): 'TWe provide an economic interpretation of the practice consisting in incorporating risk measures as constraints in portfolio optimization problem. For what we call the infimum of expectations class of risk measures, we show that if the decision maker  maximizes the expectation of a random return under constraint that the risk measure is bounded above, he then behaves as a “generalized expected utility maximizer”.  As an application, we make the link between a portfolio maximization problem, subject to Conditional Value-at-Risk being less than a threshold value, and a non-expected utility  formulation involving “loss aversion”-type utility functions.

-->February 9-->Vadori, Nelson (MS431, Department of Mathematics & Statistics, U of C): 'Smiling for the Delayed Volatility Swaps'
Abstract:
Using change of time method, we derive a closed-form formula for the volatility swap in an adjusted version of the Heston model with stochastic volatility with delay. The numerical result is presented for underlying EURUSD on September 30th 2011. The novelty of the result is two-fold: application of change of time method to the delayed Heston model and calculation of the volatility swap for this model.

-->February 3-->Hurd, Tom (McMaster U, Hamilton, ON, Canada) (Scurfield Hall, Haskayne School of Business, U of C, Friday, 2pm): 'Modelling Financial Networks and Systematic Risk'
Abstract:
The study of contagion in financial systems is very topical in light of recent events in the global markets. "Contagion" refers to the spread of defaults through a system of financial institutions, with each successive default causing increasing pressure on the remaining components of the system. The term "systemic risk" refers to the contagion-induced threat to the financial system as a whole, due to the default of one (or more) of its constituent institutions. The ultimate question for me is how mathematical models can help us understand systemic risk. In this talk I will explore some of the background concepts, then look at certain  "deliberately simplified models of systemic risk" to see what they may say about the problem.

Time
: 12-1pm): '

The Haskayne School has installed a lab of 18 student stations and one instructor station with streaming data feeds that are popular in industry: Bloomberg (10 stations) and Thomson Reuters Eikon (8 stations). Access to the lab is by ID Card, and students and Faculty can apply for use of the Lab. Access policy hasn't been settled, but there is intent that the lab should be available to Mathematical Finance students, through referral from Tony Ware or Anatoliy Swischuk.

These streaming data machines provide screens of market news and commentary (filtered by topic of interest), quotes in a broad variety of exchange-traded (TSX, NYSE, CME, NYMEX, NASDAQ, CBOE) and OTC markets (FX), and some analytics, such as implied volatility surfaces.

Both Bloomberg and Eikon feeds set up an Excel menu that allows one to structure live DDE links to live data and historic data. One can download high-frequency tick data (bid, ask, size and trade), as well as daily data for a variety of markets.

This workshop will review:
--
what data is availableh
--how to build spreadsheets that harvest the data.

-->January 19-->Swishchuk, Anatoliy (MS431) (Department of Mathematics & Statistics, U of C): Organisational meeting: schedule, annoncements, information, etc.
Abstract:
We'll be discussing our plans for this semester, Winter 2012. It includes, in particular, grad students research presentations at the Lab and PRMIA Calgary Chapter Grad Students Presentations this year (April and May 2012). Also, information about the upcoming talks of Prof. Gordon Sick (Haskayne, U of C) and Prof. Tom Hurd (McMaster U, Hamilton, ON) will be provided.

Fall 2011

This Fall 2011 we'll be doing math finance grad students research presentations (see below for more info)

************************************

-->December 7-->Yang Liu (MS569) (Department of Mathematics & Statistics, U of C
-->November 30-->Dimbi Ramarimbahoaka (MS569)
(Department of Mathematics & Statistics, U of C): 'A stochastic discount function modeled by a finite state Markov chain and related asset pricing'
Abstract:
Robert J.Elliott and John van der Hoek in 2010 investigated the theory of asset pricing using a stochastic discount function process where uncertainties in the economy are modeled by a Markov chain.
Stock price models, futures pricing etc were derived. In a later paper (2011), in the same framework, they discussed finite maturity American options where prices are obtained as solutions of a finite
dimensional variational inequality which is expressed in terms of a system of ordinary differential equation. We also give a discussion on the perpetual American option case, a recent work done
by Robert J.Elliott and myself.

-->November 23-->Matthew Couch (MS569) (Department of Mathematics & Statistics, U of C): 'Variance Swap pricing with GARCH Models'
Abstract:
A closed form variance swap strike price formula for generalized GARCH models will be presented. The generalized GARCH framework considered allows
for non-normal innovation distributions and flexible GARCH volatility specifications. We consider numerical examples with normal inverse Gaussian and normal conditional
return distributions. We further compare our results with the existing result for a continuous time GARCH limit.

-->November 16--> Paul Obour (MS569)
(Department of Mathematics & Statistics, U of C): We study pricing and hedging of Currency Translated Options (CTOs). Canadian oil producers wish to hedge (- an investment to limit loss) their production risk with futures contracts
denominated in United States dollars (USD). Evidence of this has motivated this study. CTOs are denominated in Canadian dollars (CAD) and provide various levels of currency protection
depending on the payoff structure chosen. We examine the performance of linearly delta hedging a Quanto option and discuss the pricing implication of the more efficient hedge driven by a Levy process / Copulas.

-->November 9-->
1) Steinrucke, Lea (12:00-12:30,MS569) (
Department of Mathematics & Statistics, U of C & TUM, Munich, Germany
): Since it was first introduced by Miltersen et al. (1997), Brace et al. (1997) and Jamshidian (1997), the LIBOR market model (LMM) has continuously gained in importance and popularity.
In contrast to previous approaches, the LMM focuses on modeling effective simple rates instead of continuously compounded spot or forward interest rates.
The talk will give an introduction to this seminal idea and approach of these original papers and present extensions and generalizations to the model that have been made over the last 14 years.
After a short literature review, we will in particular concentrate on models that incorporate regime-switching techniques and/or the incorporation of Markov Switching Renewal processes.
Finally, we will examine how default risk can be incorporated into the LMM.

2) Wang, Bo (12:30-13:00,MS569) (Department of Mathematics & Statistics, U of C): Asset allocation is one of the central issues in banking, finance and insurance industries. Mean – Variance, Value at Risk (VaR) and Conditional Value at Risk (CVaR)
modeling were three approaches investigated towards this issue. After introducing ruin probability and expected loss at ruin as risk measures, the optimization results became more
accurate and feasible. Using this new method, we also investigated the Solvency II problem.

(12pm, MS431)-->(Department of Mathematics & Statistics, U of C): 'My Experience as a Quant at Deloitte Paris'
Abstract:
'I worked as a Quantitative Analyst at Deloitte Paris from April 2008 to August 2011. I was a member of the Quantitative team of the Risk Advisory department (which is included in Deloitte Consulting).
My job focused on three main aspects: i)implementation of equity/FX/interest rate models for derivative pricing (with special focus on FX and equity markets); ii) theoretical review of the models used in major
banks/corporates; iii) derivative pricing for major banks/corporates. I also did some missions outside the financial derivative pricing area: Monte Carlo VaR model review (for a broker),
Capital allocation methods (for a bank) or Liquidity Gap model review (for an insurance company).'

-->October 26-->Azamed Gezahagne (12pm, MS569)-->(Department of Mathematics & Statistics, U of C): In this talk, Bayesian estimation technique on Finance, the idea of Principal Component Analysis
and Factor analysis for calibration of the Natural Gas Forward Curve will be discussed.

-->October 19-->BinBin Wang (12pm, MS569)-->(Department of Mathematics & Statistics, U of C): Abstract: I will give an overview on methodology and applications of Fourier Transform in Finance. The basic idea of derivative pricing using Fast Fourier Transform will be explained
and some selected papers will be introduced. I will also give a rough "family tree" of the development of this subject.
Remark: BiBin also kindly allowed us to post his review paper on FT on our web. See HERE.

-->October 12-->Anatoliy Swishchuk (12pm, MS569)-->(Department of Mathematics & Statistics, U of C): 'Levy Processes: History, Idesas, Applications'
Abstract:
This talk is devoted to the rich history, definitions, examples and many applications (e.g., finance, number and relativity theories, etc.) of Levy processes (stochastically continuous processes with independent and stationary increments). We'll consider in details applications of Levy processes in finance.

-->October 5 (12pm, MS569)-->Ke Zhao (Department of Mathematics & Statistics, U of C): 'In this talk, literature on Black-76 formula and Markov-modulated models will be given first. We then invoke the Markov-modulated volatility and apply it to generalize Black-76 formula.
Black formulas for Markov-modulated markets with and without jumps will be showed for two states Markov chain. Application is given using Nordpool weekly electricity forward prices.

-->September 28 (12pm, MS569)-->Swishchuk, Anatoliy (Department of Mathematics & Statistics, U of C): Abstract: We'll be discussing math finance graduate students research projects and planning their presentations for this Fall 2011.
The information about the PRMIA Calgary Chapter Grad Students Presentations next year (April, 2012) will be discussed as well.

***************************

-->September 21 (12pm, MS569)-->Juan-Pablo Ortega (Centre National de la Recherche Scientifique, Departement de Mathematiques de Besancon, Universite de Franche-Comte, France):
Abstract: Numerous empirical proofs indicate the adequacy of the time discrete auto-regressive stochastic volatility models introduced by Taylor [1986, 2005] in the description of the log-returns of financiall assets.
The pricing and hedging of contingent products that use these models for their underlying assets is a non-trivial exercise due to the incomplete nature of the corresponding market.
In this paper we apply two volatility estimation techniques available in the literature for these models, namely Kalman filtering and the hierarchical-likelihood approach, in order to implement various pricing
and dynamical hedging strategies. Our study shows that the local risk minimization scheme developed by Follmer, Schweizer, and Sondermann is particularly appropriate in this setup, especially for at and in
the money options or for low hedging frequencies.

-->September 16 (3pm, MS431)-->Eckhard Platen (University Techniology of Sydney, Sydney, Australia): 'Numerical Solutions of Stochastic Differential Equations with Jumps in Finance'
Abstract: In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables.
The numerical solution of such equations is more complex than that of those only driven by Wiener processes. The presentation builds on the recent monograph of the presenter co-authored
with Bruti-Liberati.  It provides some background on the benchmark approach for jump-diffusion markets and presents a survey and new results on higher-order methods for scenario and Monte-Carlo simulation.
Literature: E. Platen and N. Bruti-Liberati: Numerical Solution of Stochastic Differential Equations with Jumps in Finance. Springer 2010.

-->September 14 (12pm, MS 569)-->
->1) Elham Negahdary (U of C): 'Credit Risk Modeling in Energy Industry'

Abstract: Better understanding and measuring of default risk at a company level is an essential. Energy credit risk differs from that of bank credit risk in that the nature of exposures is quite different.
Unlike loans in banks, an energy company’s credit risk deals with the fulfillment of derivative deals by exchanges, and the receipt of payment for delivered goods. In Direct Energy credit risk project,
potential future exposure was simulated by correlated risk factors. Based on survival of correlated counterparties, distribution of loss was simulated to estimate expected loss, economic capital
and other credit risk metrics. Automating various risk measures gives flexibility to the model in generating scenario analyses. Concentration of risk analysis was studied based on Direct Energy’s exposure and risk limit.

->2) Wes Devauld (U of C): 'Independent Price Verification of Options on Forwards'
Abstract: The procedure of verifying an internal volatility surface with a market consensus surface constructed through a co-operative of market participants is detailed in the talk.
Using Black's model to calculate implied volatility and Delaunay triangulation to construct a surface, differences in volatility for open positions are applied to Vegas to determine mark to market profit or loss.

Summer 2011

-->August 25 (2pm, MS431)-->Zagst, Rudi (Director of the Center of Mathematics and Head of Institute for Mathematical Finance at Munich University of Technology, Munich, Germany):
Technische Universität München (TUM) is one of only six Elite-Universities in Germany and was honored for excellence in education in 2009. The Chair of Mathematical Finance is part of the Department of Mathematics at TUM and is one of the leading research centers for applied mathematical finance in Germany. The research focus lies on financial engineering, pricing of complex derivatives, risk and asset management. Teaching activities concentrate on the Master program “Mathematical Finance and Actuarial Science” as well as the elite graduate program “Finance and Information Management (FIM)”. In the first part of the talk, an overview on these two programs will be given with a special focus on FIM and the international student research exchange. In the second part, a selection of current research topics at the Chair of Mathematical Finance will be presented.

-->July 28-->Reisinger, Christoph (Mathematical and Computational Finance Group, Oxford University, Oxford, UK: http://www.maths.ox.ac.uk/contact/details/reisinge): Hamilton-Jacobi-Bellmann (HJB) Equations arise when applying Bellman's dynamic programming principle to stochastic optimisation problems. We outline the common structure of a number of applications arising in financial engineering, e.g. from European and American option valuation in incomplete financial markets. Penalty methods have been recognised as a conceptually appealing and computationally efficient method for valuing early exercise options. In this talk, we present a penalty method for HJB equations, analyse its convergence properties, and highlight the relation to state-of-the-art policy iteration methods.

*************************************************************************************************

This Fall 2010 and Winter 2011, as a part of our finance seminar, we will be reviewing the following book:
'The Volatility Surface. A Practitioner's Guide' by Jim Gatheral, Wiley/Finance, 2006.
***************************************************************************************

Winter 2011

-->April 7-->Swishchuk, Anatoliy
(Department of Mathematics & Statistics, U of C): 'Variance and Volatility Swaps in Energy Markets'

-->March 31-->Dmitrasinovic-Vidovic, Gordana & Ware, Tony (Department of Mathematics & Statistics, U of C): 'Modern Portfolio Theory-Part II'

-->March 24-->Piroozfar, Ghashang (Department of Mathematics & Statistics, U of C): Paper Review 'Games with Exhaustible Resources' by Chris Harris, Sam Howison and Ronnie Sircar
Abstract:
What we study here is the problem of declining oil reserves, and its consequences for energy supplies and prices. There exists different point of views for confronting this problem.
One way is the assumption of the few number of competitors and firms over energy market. The other way, which we are interested in the current article is the game theoretical techniques for
constructing the outcome of competition, while there exists too many various  market choices. The kind of games we will analyze, are dynamic games, since exhaustibility leads to the importance
of anticipation of changing resource impacts on prices and production.

-->March 17-->Dmitrasinovic-Vidovic, Gordana & Ware, Tony (Department of Mathematics & Statistics, U of C): 'Modern Portfolio Theory-Part I'
Abstract:
In this talk we start with the well-known, discrete time Markowiz portfolio problem, and define self-financing portfolios, tangency portfolio, and efficient frontier. We then proceed with continuous time portfolio problem and utility based optimization. We define utility and consumption functions, and standard market characteristics such are the market price of risk and risk premium in the Black –Scholes setting. We then state the Merton's portfolio problem in which an investor must choose how much to consume, and must allocate his wealth between stocks and a risk-free asset to maximize his expected lifetime utility. Finally, we present one of the major results of portfolio optimization theory, i.e.the two-fund separation theorem which states that, under appropriate conditions, every investor’s optimal portfolio is a weighted average of the market portfolio and a bond.

-->March 10-->Ware, Tony (Department of Mathematics & Statistics, U of C): Book Review : 'The Volatility Surface' by Jim Gatheral, Wiley, 2006: Chapter 11: 'Volatility Derivatives' PART II
Abstract: The second part of this talk is devoted to the valuing of volatility swaps and quadratic-variation based securities.

-->March 3-->Ware, Tony (Department of Mathematics & Statistics, U of C): Book Review : 'The Volatility Surface' by Jim Gatheral, Wiley, 2006: Chapter 11: 'Volatility Derivatives'

Abstract:
Chapter 11 focuses on the pricing and hedging of claims whose underlying is quadratic variation and presents some of the most elegant and robust results in financial mathematics, thereby explaining in part why the market in volatility derivatives is suprisingly active and liquid. The fisrt part of this was is devoted to the spanning generalized European payoffs and valuing of variance swaps.

-->February 17-->Swishchuk, Anatoliy (Department of Mathematics & Statistics, U of C): 'The valuation of the variance swaps for local Levy based stochastic volatility with delay (LLBSVD) is discussed in this talk. We provide some analytical closed forms for the expectation of the realized variance for the LLBSVD. As an applications of our analytical solutions, we fit our model to 10 years of S&P500 data (2000-01-01--2009-12-31) with variance gamma model and apply the obtained analytical solutions to price the variance swap. (This is a joint work with Kevin Malenfant).

-->Ferbruary 10-->Sezer, Deniz (Department of Mathematics & Statistics, U of C): Book Review : 'The Volatility Surface' by Jim Gatheral,
Chapter 10: Exotic Cliquets
Abstract:
Chapter 10 studies in detail three actual exotic cliquet transactions that happen to have matured so that one can explore both pricing and ex post performance. Specifically, it studies a locally capped and globally floored cliquet, a reverse cliquet, and a Napoleon.

-->February 3-->Sahmoradi, Akbar (Department of Mathematics & Statistics, U of C): The empirical studies indicate that financial data usually does not follow typical normal distribution. Our empirical investigation of front month NYMEX crude oil prices over the period from 1983:01:04 to 2010:12:14 show that the crude returns significantly deviate from normal distribution, as they show fat tails. To address this issue, a generalized hyperbolic distribution is used and its parameters are calibrated using Multi-cycle Expectation Conditional Maximization. Monte Carlo estimate of the crude European Call options is calculated. Also, the sensitivity of option prices to key parameters are investigated.

-->January 27th-->Zhao, Ke (Department of Mathematics & Statistics, U of C): Book Review : 'The Volatility Surface' by Jim Gatheral, Abstract: Chapter 9 presents various types of barrier option and show how intuition may be developed for these by studying two simple limiting cases.

-->January 20th-->Swishchuk, Anatoliy (Department of Mathematics & Statistics, U of C): Book Review : 'The Volatility Surface' by Jim Gatheral, Chapter 8: Dynamics of the Volatility Surface

Abstract: Chapter 8 shows how the dynamics of volatility can be deduced from the time series properties of volatility surface.

Fall 2010

-->December 7-->Dovoedo, Philippe (Department of Mathematics & Statistics, U of C): Book Review : 'The Volatility Surface' by Jim Gatheral,  This Chapter 7 examines the asymptotic properties of the Volatility Surface showing that all models with SV and jumps generate VS that are roughly the same shape.

-->November 30-->Cui, Kaijie (Department of Mathematics & Statistics, U of C): Paper Review: Platen E. and West J. 'A fair pricing approach to weather drivatives' Asian-Pac. Financial Markets, (2005), 11(1), 23-53.

-->November 23d-->Gezahagne, Azamed (Department of Mathematics & Statistics, U of C): Book Review : 'The Volatility Surface' by Jim Gatheral,  Chapter 6 'Modelling Default Risk'
Abstract:
This Chapter 6 applies the work on jumps (Chapter 5) to Merton's jump-to-ruin model of default; it also explains the CreditGrades model.

-->November 16-->Sezer, Denis
(Department of Mathematics & Statistics, U of C): Book Review : 'The Volatility Surface' by Jim Gatheral,  Chapter 5 'Adding jumps'
Abstract:
This Chapter 5 explores the modelling of jumps showing first why jumps are required; introduces then characteristic function techniques and applies these to the computation of IV in models with jumps; concludes by showing that the SVJ (SV with jumps in the stock price) is capable of generating a volatility surface that has most of the features of the empirical surface.

-->November 9-->Ware, Tony (Department of Mathematics & Statistics, U of C): Accurate semi-Lagrangian time stepping for gas storage problems’
Abstract:
Stochastic dynamic programming approaches for the valuation of natural gas storage, and the determination of the optimal continuous-time injection/withdrawal strategy, give rise to HJB P(I)DEs which are typically solved using finite differences  [Thompson et. al., 2009].  A semi-Lagrangian discretization was analyzed by [Chen and Forsyth, 2007], who demonstrated first-order convergence to the viscosity solution.This talk will show how a semi-Lagrangian approach for such problems can be formulated in such a way that it generates a second-order accurate discretization in time. Combined with a hybrid Fourier/finite difference discretization in the remaining dimensions, the resulting method can provide efficiency gains over existing approaches.

-->November 2-->Swishchuk, Anatoliy (Department of Mathematics & Statistics, U of C): Book Review : 'The Volatility Surface' by Jim Gatheral,
Chapter 4 'The Heston-Nandi Model'
Abstract:
In this Chapter 4, author chooses specific numerical values for the parameters of the Heston (1993) model, $\rho=-1$ as originally studied by Heston and Nandi (1998) and demonstrates that an approximate formula for implied volatility derived in Chapter 3 works particularly well in this limit. As a result, they are able to find parameters of LV and SV models that generate almost identical European option prices.

-->October 26-->1) Badescu, Alex (Department of Mathematics & Statistics, U of C): Book Review : 'The Volatility Surface' by Jim Gatheral,
Chapter 3:
'The Implied Volatility Surface'
Abstract:
In Chapter 3, author derives a powerful representation for implied volatility (IV) in terms of local volatility and applies this to build intuition and derive some properties of the implied volatility surface
(VS) generated by the Heston model and compare with the empirically observed SPX surface; deduces that SV cannot be the whole story.

2) Swishchuk, Anatoliy

-->October 20--> Dr. Sebastian Sager (Interdisciplinary Center for Scientific Computing (IWR), University of Heidelberg, Germany): 'Optimization with Differential Equations: Algorithms and Applications'
Abstract:
Scientific computing with its core components mathematical modeling, simulation, and optimization has developed into a key technology for understanding and mastering challenges in science and engineering.
Problems as diverse as the design and operation of chemical production plants, economic decision making, the understanding of the dynamics of cancer, or the optimal control of autonomous cars all require strong
cross-disciplinary efforts supported by mathematical and computational methods. The generically interdisciplinary approach of scientific computing is generally considered a third pillar of science, complementary
to experiment and theory. It has already become a standard in physics, chemistry and engineering and is currently entering research in the life sciences and economics. We will survey recent developments in the optimization
with differential
equations and discuss parameter estimation, optimum experimental design, and optimal control, with a focus on integer control functions. We present fast and reliable deterministic algorithms that are based on derivative information. We will present several applications from different application fields.

(Department of Mathematics & Statistics, U of C): Book Review : 'The Volatility Surface' by Jim Gatheral,
Chapter 3:
'The Implied Volatility Surface'
Abstract:
In Chapter 3, author derives a powerful representation for implied volatility (IV) in terms of local volatility and applies this to build intuition and derive some properties of the implied volatility surface
(VS) generated by the Heston model and compare with the empirically observed SPX surface; deduces that SV cannot be the whole story.

-->October 12-->Swishchuk, Anatoliy
(Department of Mathematics & Statistics, U of C):
'Approximations of Security Markets by Geometric Markov Renewal Processes (GMRP)' . Part I: Definition of GMRP, Martingale Properties and Averaging of GMRP

ABSTRACT: This talk is devoted to the study of discrete Markov-modulated (B,S)-security markets which are described by geometric Markov renewal processes (GMRP).
We study their martingale properties and derive Markov renewal equation for expectation.We also study GMRP in series scheme.
We state averaging, merging, diffusion approximation, normal deviations and Poisson approximation results for such models.
These limit models can be used for approximations of regime-switching security markets. We state the option pricing formula for GMRP as well.

-->October 5th-->Ware, Tony (Department of Mathematics & Statistics, U of C):
Book Review: 'The Volatility Surface. A Practitioner's Guide' by Jim Gatheral
Chapter 2: The Heston Model

-->September 28th-->Couch, Matthew (Dept Math & Stat, U of C): Variance and Volatility Swaps in stochastic volatility models based on Levy processes.
Abstract: We present a brief review of Levy process based asset price modeling and some of the better known stochastic volatility models based on Levy processes.
The quadratic variation process is considered as a measure of asset price volatility in non-Gaussian models. We show how the fair strike price for Variance and Volatility
swaps may be calculated in such models through the quadratic variation process.

-->September 21st-->Swishchuk, Anatoliy (Department of Mathematics & Statistics, University of Calgary):
Book Review: 'The Volatility Surface. A Practitioner's Guide' by Jim Gatheral
Chapter 1: Stochastic Volatility and Local Volatility

Summer 2010

-->June 17th-->Cohen, Samuel (University of Adelaide, Australia):  'BSDEs in Discrete time and their extensions '
Abstract: BSDEs (Backward Stochastic Differential Equations) are increasingly important equations in many areas of mathematical finance and stochastic control. In this talk we shall explore BSDEs in discrete time finite state systems, where many strong results can be obtained very simply. Using this, we shall give a representation of all time-consistent nonlinear expectations in this context. We shall then discuss extensions of this theory to infinitely many outcomes, and to general probability spaces in continuous time.
Example

-->June 10th-->Rodrigo, Marianito (Instituto Tecnologico Autonomo de Mexico (ITAM), Mexico): 'American options with time-varying parameters via Mellin
transforms'

Abstract: We use a Mellin transform approach to address the American option valuation problem under a time-dependent Black-Scholes modeling framework. The value of the put is calculated first, and then we establish a quasi put-call parity relation for American options to determine the value of the corresponding call. Since the integral equation for the free boundary is not solvable, we provide an approximating ordinary differential equation satisfied by the optimal exercise price. For the constant-parameter case, the ordinary differential equation is analytically tractable. An examination of the delta and pricing errors in our numerical experiments reveals that the proposed approach is remarkably robust and accurate.

Winter 2010

-->April 1st-->Swishchuk,  Anatoliy
(Department of Mathematics & Statistics, U of C):

Abstract: In this talk, we study financial markets with stochastic volatilities driven by fractional Brownian motion with Hurst index H>1/2. Our models include fractional versions of Ornstein-Uhlenbeck,
Vasicek, geometric Brownian motion and continuous-time GARCH models. We price variance and volatility swaps for above-mentioned models. (Joint work with Yu. Mishura)

-->March 25th-->Dmitrasinovich-Vidovich, Gordana & Ware, Tony
(Department of Mathematics & Statistics, U of C): 'Portfolio Optimization Under Downside Risk Measures'

Abstract:
We give an overview of our work on portfolio optimization with respect to various downside risk measures, including Value at Risk, Capital at Risk, and Conditional Capital at Risk (or Expected Shortfall). In some cases we are able to give explicit formulae for the optimal investment strategy. We consider portfolios of lognormal assets, as well as portfolios containing mean-reverting assets.

->March 18th-->Malenfant, Kevin & Swishchuk, Anatoliy (Department of Mathematics & Statistics, U of C): 'Analysis of Temperature Derivatives' (Chapter 10)
Book Review: 'Stochastic Modelling of Electricity and Related Markets' by F. Benth, J. Benth and S. Koekebakker, 2008, World Sci.)

2) Swishchuk, Anatoliy: "Analysis of Temperature Derivatives' (Chapter 10, sec. 10.3-10.4)

Abstract: The Chapter 10 is devoted to the market for temperature futures. We present continuous-time mean reversion models being generalizations of autoregressive moving average time series.
Applying these to temperature data, we find that the 'volatility' of temperature has a clear seasonal pattern. The temperature models allow for rather explicit pricing of the typical futures traded on CME.
The chapter includes a thorough empirical analysis of Stockholm temperature data in view of the proposed models.
Sec. 10.1-10.2 will be presented by K. Malenfant and 10.3-10.4-by A. Swishchuk

->March 11th-->Swishchuk, Anatoliy (Department of Mathematics & Statistics, U of C): 1) 'Modelling of Electricity Futures Markets' (Chapter 8, sec. 8.5-8.8)
Here is the pdf-file with Tables and Figures

' (Chapter 10, sec. 10.1-10.2)
Book Review: 'Stochastic Modelling of Electricity and Related Markets' by F. Benth, J. Benth and S. Koekebakker, 2008, World Sci.)

Abstract: The Chapter 10 is devoted to the market for temperature futures. We present continuous-time mean reversion models being generalizations of autoregressive moving average time series.
Applying these to temperature data, we find that the 'volatility' of temperature has a clear seasonal pattern. The temperature models allow for rather explicit pricing of the typical futures traded on CME.
The chapter includes a thorough empirical analysis of Stockholm temperature data in view of the proposed models.

-->March 4th-->Ware, Tony
(Department of Mathematics & Statistics, U of C): 'Pricing and Hedging of Energy Market' (Chapter 9)
Book Review: 'Stochastic Modelling of Electricity and Related Markets' by F. Benth, J. Benth and S. Koekebakker, 2008, World Sci.

Abstract: Chapter 9 presents pricing formulas for call and put options based on the various proposed spot forward and swap models. The options prices become generalizations of the
Black-76 formula when the underlyingmodels are depending on Brownian motions only. For models with jumps, a Fourier approach is used to derive formulas for the prices. Issues
of hedging are discussed for these options. The pricing of spread and Asian options are analyzed for arithmetic multi-factor models, where reasonably explicit formulas are available
based on the cumulant functions of the jump processes. A case study on the pricing of spark spread options in the UK market is presented, based on a direct modeling approach for the

-->February 25th-->Swishchuk, Anatoliy (Department of Mathematics & Statistics, U of C): 'Modelling of Electricity Futures Markets' (Chapter 8)
Book Review: 'Stochastic Modelling of Electricity and Related Markets' by F. Benth, J. Benth and S. Koekebakker, 2008, World Sci.)
Abstract:  The smoothing algorithm from Chapter 7 is applied to analyse the Nord Pool electricity futures market using HJM-based models. A principal component analysis reveals certain structures
for the short- and long-term market, and motivate a parametric multi-factor market model, including seasonal volatility with maturity effect. The model is fitted to market data.

-->February 18th-->No 'Lunch at the Lab'-Reading Week

-->February 11th-->
Zhao, Ke
(Department of Mathematics & Statistics, U of C): Three Papers' Review by F. Benth et al. (2005-2007)
Ke Zhao's Talk file is here.

-->
February 4th
-->Swishchuk, Anatoliy (Department of Mathematics & Statistics, U of C): 'The valuation of the variance swaps for local stochastic volatility with delay and jumps is discussed in this talk. We provide some analytical closed forms for the
expectation of the realized variance for the stochastic volatility with delay and jumps. Besides, we also present a lower bound for delay as a measure of risk.  As applications
of our analytical solutions, numerical examples using S&P60 Canada Index (1998-2002) and S&P500 Index (1990-1993) are then provided to price variance swaps with delay and jumps.

-->January 28th-->Ware, Tony (Department of Mathematics & Statistics, U of C): 'Constructing Smooth Forward Curves in Electricity Markets' (Chapter 7)
(
Book Review: 'Stochastic Modelling of Electricity and Related Markets' by F. Benth, J. Benth and S. Koekebakker, 2008, World Sci.)
Abstract: When applying the HJM approach (Chapter 6) to electricity markets, one may base the electricity futures price dynamics on a model for non-traded forwards.
To estimate such models, one needs to derive forward data from the observed electricity futures prices. An algorithm for the derivation of smooth forward curves in electricity markets is presented in Chapter 7.
The algorithm may be applied to gas market as well. We demonstrate the algorithm at work on Nord Pool electricity futures data, and further apply it to study the term structure of volatility of electricity.

-->January 21st-->Swishchuk, Anatoliy (Department of Mathematics & Statistics, U of C): 'Modelling Forwards and Swaps Using the Heath-Jarrow-Morton (HJM)
Approach (Chapter 6)
(Book Review: 'Stochastic Modelling of Electricity and Related Markets' by F. Benth, J. Benth and S. Koekebakker, 2008, World Sci.)

Abstract: The HJM approach to the modelling of forward and swap prices is presented in this Chapter 6. The different modelling issues regarding forward prices and swaps are investigated in detail,
along with theincorporation of jump processes. As we show, the no-arbitrage condition for the term structure dynamics of the swap price rules out most of the relevant models.
To resolve this issue, we introduce market models for the swaps, much in the spirit of LIBOR models for fixed income markets.

Fall 2009

This Fall 2009, as a part of our finance seminar, we are reviewing the following book:
'Stochastic Modeling of Eelectricity and Related Markets' by F. Benth, J. Benth and S. Koekebakker, 2008, World Sci. Publ.

-->December 9th-->Surkov, Vladimir (Department of Mathematics, University of Western Ontario, London, ON): 'Pricing and Hedging of Commodity
Derivatives using the Fast Fourier Transform '
Abstract:
Energy commodities, such as oil, gas and electricity, exhibit high volatilities, have sudden price jumps and tend to revert to a long run equilibrium. This talk develops a Fast Fourier Transform-based
method for valuing and hedging of contingent claims written on mean-reverting processes with jumps. The Mean-Reverting Fourier Space Time-stepping (mrFST) method developed in this talk solves the
option pricing partial integro-differential equation (PIDE) by applying the Fourier transform to obtain an explicitly solvable linear system of ordinary differential equations. Solving the PIDE in Fourier space
allows for the integral term to be handled efficiently and avoids the asymmetrical treatment of diffusion and integral terms, common in the finite difference schemes found in the literature. For path-independent
options, prices can be obtained for a range of spot prices in one iteration of the algorithm. For exotic, path-dependent options, a time-stepping methodology is developed to handle free boundaries and
exercise policies. Finally, an efficient methodology for computing the various option Greeks is developed for use in conjunction with dynamic and static hedging in the presence of jumps.

-->December 2nd-->Zinchenko, Yuriy (Department of Mathematics & Statistics, U of C): 'Optimization in financial engineering'
Abstract:
We will survey the use of optimization techniques in the context of financial engineering. In particular, we will discuss the so-called
portfolio optimization problem that corresponds to optimal asset allocation, and the problem of pricing derivative securities.
No optimization background will be assumed.

-->November 25th-->Ware, Tony (Department of Mathematics & Statistics, U of C): Book Review: 'Stochastic Modeling of Electricity and Related Markets'
by F. Benth, J, Benth and S. Koekebakker, 2008, World, Sci. Publ.; Chapter 5: 'Applications to the Gas Markets'

-->November 18th-->Swishchuk, Anatoliy (Department of Mathematics & Statistics, U of C): Book Review: 'Stochastic Modeling of Electricity and Related Markets'
by F. Benth, J. Benth and S. Koekebakker, 2008, World Sci. Publ.; Chapter 4: 'Pricing of Forwards and Swaps Based on the Spot Price', Sec. 4.3-4.4

-->November 11th: Reading Day-No Lunch at the Lab

-->November 4th-->Nedunthally, Thomas (Department of Mathematics & Statistics, U of C): 'A new approach to modelling the Natural Gas futures curve and Levy based models'

Abstract: In this talk, we discuss modelling the natural gas futures curve by first using a regression equation to seperate the seasonality and the underlying curve. A two factor model based on Pilipovic,
Xu with spot prices and a long run mean is used to compute the futures price. The long run mean, which also tells us if the curve is in contango or backwardation, is revealed through the underlying futures
curve using a procedure we shall discuss. This allows for more accurate simulations of the gas spot price through the two factor model, and lets us capture the dynamics of the futures curve. Levy-based
one factor OU type models using alpha stable and NIG processes are also introduced. The calibration of these models are also discussed.

-->October 28th-->Swishchuk, Anatoliy (Department of Mathematics & Statistics, U of C): Book Review: 'Stochastic Modeling of Electricity and Related Markets'
by F. Benth, J. Benth and S. Koekebakker, 2008, World Sci. Publ.; Chapter 4: 'Pricing of Forwards and Swaps Based on the Spot Price', Sec. 4.1-4.2

-->October 21st-->Couch, Matthew (Department of Mathematics & Statistics, U of C): 'Variance and Volatility Swaps for the COGARCH(1,1) Model'
Abstract: In this talk, we present variance and volatility swaps valuations for the COGARCH (1,1) model intriduced by Kluppelberg, Lindner and Maller (2005).
We consider two numerical examples: for compound Poisson COGARCH(1,1) and for variance gamma COGARCH(1,1) processes. Also, we demonstrate two different situations for the volatility swaps:
with and without convexity adjustment to show the difference in price values.

-->October 14th-->Ware, Tony (Department of Mathematics & Statistics, U of C): Book Review: 'Stochastic Modeling of Electricity and Related Markets'
by F. Benth, J, Benth and S. Koekebakker, 2008, World, Sci. Publ.; Chapter 3: 'Stochastic Models for Energy Spot Price Dynamics'

-->October 7th-->Swishchuk, Anatoliy (Department of Mathematics & Statistics, U of C): 'Pricing of Variance and Volatility Swaps with Semi-Markov Volatilities'
Abstract: In this talk, we introduce a general class of semi-Markov processes and model a stock price with stochastic volatility (SV) that depends on the semi-Markov process (we call it semi-Markov volatility).
We price variance and volatility swaps for the SV driven by the semi-Markov process. We also discuss some extensions of the obtained results such as local semi-Markov volatility (LSMV),
Dupire formula for LSMV and residual risk associated with the swap pricing with LSMV.

-->September 30th-->Swishchuk, Anatoliy (
Department of Mathematics & Statistics, U of C): Book Review: 'Stochastic Modeling of Electricity and Related Markets'
by F. Benth, J, Benth and S. Koekebakker, 2008, World, Sci. Publ.; Chapter 2: 'Stochastic Analysis for Independent Increment Processes'

-->September 23d-->Badescu, Alexandru (Department of Mathematics & Statistics, U of C): 'Bond Valuation Under Discrete-Time Regime-Switching Term-Structure
Models'

Abstract: We propose a discrete-time, Markov, regime-switching, affine term structure model for valuing bonds and other interest-rate securities.
The proposed model incorporates the impact of structural changes in (macro)-economic conditions on interest rate dynamics. It also has some
econometric advantages compared to its continuous-time counterpart. The market in the proposed model is, in general, incomplete. We introduce a
modified version of the Esscher transform, namely, a double Esscher transform, to specify a price kernel so that both market and economic
risks are taken into account. We provide a simple and streamlined way to derive exponential-affine forms of bond prices using backward induction.
(Joint work with Robert J. Elliott and Tak Kuen Siu)

-->September 16th-->Ware, Tony (Department of Mathematics & Statistics, U of C)

Spring-Summer 2009

->July 16th-Mishura, Yuliya (Kiev National University, Ukraine):

Abstract: Financial markets fairly often have a long memory and it is a natural idea to model them with the help of fractional Brownian motion (fBm) or some of its modifications.
However, it is not so straightforward to implement because the market model is appropriate when it does not admit arbitrage and the models involving fractional Brownian motion are
not arbitrage-free. The talk is devoted to some methods of construction of the long-memory arbitrage-free models and to the discussion of different approaches to
this problem. In particular, we introduce the mixed Brownian-fractional-Brownian model and establish conditions that ensure the absence of arbitrage in such a model.
Also we consider a fractional version of the Black-Scholes equation for the mixed Brownian-fractional-Brownian model which contains pathwise integrals w.r.t. fBm,
discuss possible applications of Wick products in fractional financial models and produce Black-Scholes equation for the fractional model involving Wick product w.r.t. fBm.
References
[1] Biagini, F., Hu, Y., Oksendal, B., Zhang T.: Stochastic Calculus for Fractional Brownian Motion and Applications. Probability and Its Applications, Springer (2008).
[2] Mishura, Yu. S.: Stochastic Calculus for Fractional Brownian Motion and Related Processes. Lecture Notes in Mathematics 1929, Springer (2008).

->June 29th-
Gupta, Alok (Oxford University, UK): Calibration Using Consistent Bayesian Estimators
ABSTRACT: The general calibration problem in financial models is considered.
We reformulate the problem into a Bayesian framework to attain posterior distributions for calibration parameters.
We show that, for any continuous and bounded loss function, the corresponding Bayesian estimatoris consistent.
Finally we work through numerical examples to clarify theconstruction of Bayesian posteriors and its uses.
The main focus is on the local volatility model.

->May 19-Jaimungal, Sebastian (U of Toronto):  'Energy commodities, such as oil, gas and electricity, lack the liquidity of equity markets, have large costs associated with storage, exhibit high volatilities and can have significant spikes in prices. Furthermore, and possibly most importantly, commodities tend to revert to long run equilibrium prices. Many complex commodity contingent claims exist in the markets, such as swing and interruptible options; however, the current method of valuation relies heavily on Monte Carlo simulations and tree based methods. In this talk, I will describe a new model of cointegrated prices containing mean-reverting jumps and diffusions as well as a new valuation framework by working in Fourier space. The method is based on the Fourier space time-stepping algorithm of Jackson, Jaimungal, and Surkov (2008), but is tailored for mean-reverting models. I will demonstrate the utility of the method by applying it to the valuation of European, American, Spread and swing options. In addition, I will discuss the real option to invest in an oil field where the volume is stochastic but is discovered as time evolves.[ This is based on joint work with Vladimir Surkov, Ph.D. candidate, Dept. Computer Science, U. Toronto]

Winter 2009

->April 30-Yalamova, Rossitsa (U of Lethbridge): 'Explaining What Leads Up to Stock Market Crashes: A Phase Transition Model and Scalability Dynamic'

Abstract: The market crash as phase transition in Johansen and Sornette (1999) points at the analogy between the three states of a physical system (solid, liquid and gas) and stock market dynamics at a "microscopic" level, where the individual trader has only three possible actions: selling, buying or waiting.  According to this model at the critical point order prevails in the market as all traders have the same opinion sell which leads to “significant drawdowns”. We do not offer an alternative to EMH/CAPM but extend the existing framework to accommodate situations with higher information complexity, interactions with positive feedback, and extreme events that cannot be simply explained by presuming independent-additive data point, and normal distributions.
This is joint work with Bill McKelvey, UCLA Anderson School of Management (paper)

->April 2nd-Salisbury, Thomas (York U, Toronto): 'Equity guarantees and retirement'
Abstract: A new generation of retirement savings products offer the upside associated with equity returns, coupled with the downside protection of annuities. I will describe the changing demographics of
retirement planning, and some of the products created to serve this market. Also some of the mathematical problems associated with hedging, pricing, and managing portfolios that incorporate these
guaranteed living benefits. This talk describes joint work with Huaxiong Huang and Moshe Milevsky.

->26 March-Kitchen, Clifford (U of C): 'Applications of the Normal Inverse Gaussian (NIG) Processes in Mathematical Finance'

Abstract: Many of the papers we have discussed in this lab use L\'{e}vy driven stochastic process rather than the usual Gaussian type.
These models are typically complex and empirical results are shown with little detail of how to calibrate and implement the model.

The intent here is give the introductory steps required to complete this work. I will show how to incorporate a L\’{e}vy process by modeling,
calibrating and pricing European options using a basic NIG process.

->19 March-Nedunthally, Thomas (U of C):
Paper Review:
Stochastic Models of Natural Gas Prices and Applications to Natural Gas Storage Valuation (Chen and Forsyth, 2007)
Abstract: Two one factor models with regime switching are introduced in this paper to mimic the behaviour of two-factor models that have been previously
developed to model natural gas spot prices. Calibration results for the regime switching model show the ability to capture both the long term and short term dynamics of market futures prices.
The calibrated models are then used to price a natural gas storage facility.

->5 March-
Couch, Matthew (U of C):
'Paper review on regime-switching models with applications in finance'

Abstract:
We review selected sections of early papers developing Markov chain based regime switching time series models.
We also review the paper ‘Pricing Volatility Swaps Under Heston’s Stochastic Volatility Model with Regime Switching’
by Robert J. Elliott, Tak Kuen Siu, Leunglung Chan, 2005. In this paper a model is developed for pricing volatility derivatives,
such as variance swaps and volatility swaps under a continuous-time Markov-modulated version of the stochastic volatility (SV)
model developed by Heston.

-
>26 February-Sheriff, John (U of Lethbridge): '

Abstract: The use of Levy processes and related models is an attractive option in mathematical finance due to their ability to more accurately capture observed market behavior.
However, this comes at the price of greater complexity and the associated challenge of fitting a more complex model to market data.  One approach to meeting
this challenge is to employ evolutionary algorithms, an iterative procedure that relies upon mutation, propagation, and selection to estimate important model parameters.
The talk will address the use of such algorithms in the context of fitting jump-diffusion models to market data.

->15-22 Feb-Reading Week (No 'Lunch at the Lab')

-
>12 February
-Malenfant, Kevin (U of C): Paper Review: 'Analysis of Valuation Formulae and Applications to Exotic Options in Levy Models' by E. Eberlein, K. Glau & A. Papapantoleon

Abstract: Paper discusses the valuation problem for a broad spectrum of plain vanilla and path-dependent options in a general modeling framework,
and specifically for Levy driven models. Among the derivatives which paper considers are digitals, double digitals, asset-or-nothing options,
self-quantos, lookback and one-touch options.

->5 February-Powojowski, Miro (NBC, Canada): 'Some observations on implied volatility'
Abstract:
The observed departures of real world markets from the Black-Scholes model have generated much research activity in academic
circles and many practical attempts at handling the problem in industry. With some exceptions, the two groups chose very different approaches to
the problem. While academics have been building more complex models based on more general processes for underlying assets, practitioners
have focused on building ad-hoc corrections to the Black-Scholes models. Both have been adding parameters to the basic model, the academics
preferring internal model consistency over the ease of parameter estimation, while finance professionals making the exact opposite
tradeoffs. In this talk I will present some theoretical arguments justifying the industry practice of using implied volatilities as a
basis for pricing and hedging options.

->29 January
-Swishchuk, Anatoliy (U of C):
'Multi-Factor Levy Models II: Pricing of Financial and Energy Derivatives'

Abstract: This talk is devoted to the multi-factor Levy models and their applications in financial and energy derivatives' pricing.
The first part 'Multi-Factor Levy Models I: Alpha-Stable Levy Processes'
(http://finance.math.ucalgary.ca/papers/LaLTalk22Jan09.pdf) (Jan 22) introduced and described alpha-stable Levy processes and based on them multi-factor Levy models.
The second part 'Multi-Factor Levy Models II: Pricing of Financial and Energy Derivatives' (Jan 29) will be devoted to the applications of multi-factor Levy models in financial a
nd energy derivatives' pricing. We'll consider swaps, interest rate derivatives, forward and futures pricing. The approach is based on change of time for alpha-stable Levy processes.

->22 January-Swishchuk, Anatoliy (U of C): 'Multi-Factor Levy Models I: Symmetric Alpha-Stable (SaS) Levy Processes'

Abstract: This talk is devoted to the multi-factor Levy models and their applications in financial and energy derivatives' pricing, and consists of two parts.
The first part 'Multi-Factor Levy Models I: Alpha-Stable Levy Processes' introduces and describes alpha-stable Levy processes and based on them multi-factor Levy models.

The second part 'Multi-Factor Levy Models II: Pricing of Financial and Energy Derivatives' (next seminar) will be devoted to the applications of multi-factor Levy models in financial and energy derivatives' pricing.

Fall 2008

->12th November-Ware, Tony (Department of Math & Stat, U of C):  Fourier transform methods are well-suited to the computation of expectations of functions of Levy processes (such as Poisson jump-diffusion, or Variance Gamma processes), and thus they often form the basis of methods for numerical option pricing when the underlying asset follows a Levy process. In this talk I will review these methods, and show how, by use of semi-Lagrangian time-stepping and the non equally-spaced fast Fourier transform (NFFT), they can be extended to mean-reverting and other processes with Levy random shocks. Numerical examples will be provided. (Joint work with Li Xu).

->5th November-Nedunthally, Thomas (Department of Math & Stat, U of C): by Rene Carmona and Michael Ludkovski
Abstract:
This paper reviews the literature of spot convenience yield models, and analyzes in detail two new extensions. First, discussion a variant of the Gibson-Schwartz model with time-dependent parameters. Second, description a new three-factor affine model with stochastic convenience yield and stochastic market price of risk.

->29th October -Swishchuk, Anatoliy  (Department of Math & Stat, U of C): ' In the second part of this talk we describe the second approach in pricing of Levy-based interest rate derivatives based on partial integro-differential equations (PIDEs). We show how to price zero-coupon bonds and bond options. Also, we present PIDEs for pricing of swaps, caps, floors and options on them, swaptions, captions and floortions, respectively. (In the first part of this talk we described the first approach in pricing of Levy-based interest rate derivatives based on change of time method for alpha-stable Levy processes).

->22nd October-Swishchuk, Anatoliy (Department of Math & Stat, U of C): 'We describe two approaches in pricing of Levy-based interest rate derivatives. The first approach is based on change of time method for alpha-stable Levy processes. The second approach is based on partial integro-differential equations (PIDEs). We show how to price zero-coupon bonds and bond options. Also, we present PIDEs for pricing of swaps, caps, floors and options on them, swaptions, captions and floortions.

->
15th October-Deniz Sezer (Department of Math & Stat, U of C):
In this talk I will present recent results on Markov Chain convergence based on joint work with Neal Madras.  Let P_n^x, and \pi be respectively the n-step transition probability kernel and the stationary distribution of a Markov chain.  In many applications it is desirable to have a quantitative bound for convergence of P_n^x to \pi, i.e. a bound of the form d(P_n^x,\pi)<g(x,n) where d is a metric on the space of probability measures and g is a function which can be computed explicitly.  In continuous state spaces one way to obtain a quantitative bound is formulating the Markov chain as an iterated system of random maps and applying David Steinsaltz's local contractivity convergence theorem.  If the conditions are satisfied, this theorem yields a quantitative bound in terms of Wasserstein distance.  We first develop a systematic framework to check for the conditions of Steinsaltz's theorem, and then show how one can obtain a quantitative bound in terms of total variation distance from a quantitative bound in terms of Wasserstein distance.

->8th October-Kevin Malenfant (Department of Math & Stat, U of C): Paper Review: 'An Introduction to Levy Processes with Applications in Finance' by Antonis Papapantoleon (Vienna University of Technology, Vienna, Austria)
Abstract:
This paper aims at introducing Levy processes in an informal and intuitive way, accessible to non-specialists in the field.

->1st October-Sivia Mayoral (University of Madrid, Spain): '

->24th September-Matt Lyle
This paper presents a method for valuing power derivatives using a supply-demand approach. Our method extends work in the field by incorporating randomness into the base load portion of the supply stack function and equating it with a noisy demand process. We obtain closed form solutions for European option prices considering two different supply models: a mean-reverting model and a Markov chain model. The results are extensions of the classic Black-Scholes equation. The model provides a relatively simple approach to describe the  complicated price behaviour observed in electricity spot markets and also allows for computationally efficient derivatives pricing.

->17th September-Deniz Sezer (Department of Math & Stat, U of C): I will talk about a reduced information model for credit risk.  In this model, the time when a company claims bankruptcy is the hitting time of the asset value process of the company, denoted by X_t,  to a default threshold.  The market can not observe X_t prior to bankruptcy,   however it can observe R(X_t) , where R(x)=i , if x_i<x<x_{i+1}, where x_1,...x_N are certain thresholds.  I will explain how we derive zero coupon bond prices and default intensities when the X process is a diffusion.  In the time remaining I will discuss open questions and future directions related to this model.

(Based on joint work with Robert Jarrow and Philip Protter).

Spring-Summer 2008

->19th June-
Malyarenko, Anatoliy
(Deprtment of Mathematics & Physics, Malardalen University, Vasteras, Sweden): 'Analytical Finance Package '
Abstract:
We describe the Java package afp that contains a collection of applets in the area of analytical finance.
The user of the package is able to price different financial instruments using Monte Carlo simulation, finite difference methods etc.

->12th June-Neduthally, Thomas (Department of Math & Stat, University of Calgary, Calgary,Canada): Paper's Review: 'Gas Storage Valuation Using a Monte Carlo Method' by A. Boogert & C. de Jong (BWPEF 0704, December 2006, Birkbeck, University of London)

->22nd May-Silvestrov, Dmitrii (Deprtment of Mathematics & Physics, Malardalen University, Vasteras, Sweden): 'Optimal Pricing of American Type Options for Modulated Price Processes'
Abstract: This lecture presents a survey of the latest results on option optimal pricing for modulated price processes achieved by the author and his collaborators. These results are: discovery of multi-threshold structure  of  optimal stopping strategies for option models with general convex payoffs and formulation of conditions, which implicate multi- and one-threshold structures for optimal stopping strategies; introduction and investigation of new models of pricing processes modulated by semi-Markov market indices; obtaining of skeleton approximations, uniform with respect to a perturbation parameter, for continuous- and discrete-time option pricing models; finding of new effective general conditions for convergence of option reward functions; constraction of effective Monte Carlo algorithms for pricing of options based on information about structure of optimal stopping domains, experimental software for pricing of options, and the latest achievements are connected with stochastic models for reselling of options.

->15th May-Swishchuk, Anatoliy (Department of Math & Stat, University of Calgary, Calgary,Canada): Review of Wim Schoutens book 'Levy Processes in Finance. Pricing Financial Derivatives', Wiley, 2003: Chapter 10 'Interest-Rate Models'

->2nd May-'Lunch at the Lab' in conjuction with  North/South Dialog Meeting (Friday-Saturday, May2-3, U of C): Mathematical Finance Session (U of C, MS431, Friday, May2, 1:00pm-5:30pm)

Winter 2008

->24th Apr-Ware, Tony
(Department of Math & Stat, University of Calgary, Calgary,Canada): Review of Wim Schoutens book 'Levy Processes in Finance. Pricing Financial Derivatives', Wiley, 2003:  Chapter 8 'Simulation Techniques', sec.8.4 'Simulation of Particular Processes'

(Department of Math & Stat, University of Calgary, Calgary,Canada): Review of Wim Schoutens book 'Levy Processes in Finance. Pricing Financial Derivatives', Wiley, 2003: 'Simulation of Generalized Hyperbolic Processes'

->10th Apr-Swishchuk, Anatoliy  (Department of Math & Stat, University of Calgary, Calgary,Canada): Review of Wim Schoutens book 'Levy Processes in Finance. Pricing Financial Derivatives', Wiley, 2003:  Chapter 8: 'Simulation Techniques', Sections 8.1-8.3.

->3d Apr-Swishchuk, Anatoliy  (Department of Math & Stat, University of Calgary, Calgary,Canada): Review of Wim Schoutens book 'Levy Processes in Finance. Pricing Financial Derivatives', Wiley, 2003:  Chapter 7: 'Levy Models with Stochastic Volatility'

->27th Mar-Pang, James
(Department of Math & Stat, University of Calgary, Calgary,Canada): Value, Trading Strategies and Financial Investment of Natural Gas

->20th Mar-Swishchuk, Anatoliy  (Department of Math & Stat, University of Calgary, Calgary,Canada): Review of Wim Schoutens book 'Levy Processes in Finance. Pricing Financial Derivatives', Wiley, 2003: Section 5.4.-5.5.: 'Adding an Additional Term' and 'Examples of OU Processes'& Chapter 6: 'Stock Price Models Driven by Levy Processes'

->13th Mar-Badescu, Andrei (Department of Statistics, University of Toronto, Toronto, ON, Canada):
'Return Probabilities of Stochastic Fluid Flows and Their Use in Collective Risk Theory'

->6th Mar-Swishchuk, Anatoliy (Department of Math & Stat, University of Calgary, Calgary,Canada): Chapter 5: 'Levy Processes and OU Processes', section 5.3. Examples of Levy proceses

->28th Feb-Matt Lyle (Haskayne School of Business, U of C), Liangkun Li, Akbar Shahmoradi (Department of Math & Stat, University of Calgary, Calgary,Canada):

1) Review of Rama Cont's paper: Empirical properties of asset returns:
stylized facts and statistical issues (Quant. Finance, 2001, 1, pp.1-14).

2) Review of Wim Schoutens's book "Levy Processes in Finance. Pricing Financial Derivatives" (Wiley, 2003): Chapter 4: "Imperfections of the Black-Scholes Model".

->14th Feb-Ware, Tony (Department of Math & Stat, University of Calgary, Calgary, Canada): Chapter 5: Levy Processes and OU Proceses, sections 5.1. 'Levy Processes' and 5.2. 'OU Processes'.

->7th Feb-Swishchuk, Anatoliy (Department of Math & Stat, University of Calgary, Calgary, Canada): Chapter 3: The Black-Scholes Model

->31st Jan-Badescu, Alexandru (Department of Math & Stat, University of Calgary, Calgary, Canada): Chapter 2: Financial Mathematics in Continuous Time

->24th Jan-Swishchuk, Anatoliy (Department of Math & Stat, University of Calgary, Calgary, Canada): Review of Wim Schoutens book 'Levy Processes in Finance. Pricing Financial Derivatives', Wiley, 2003; Contents, Chapter I: Introduction

Fall 2007

->22th Nov-Orosi, Greg (Department of Math & Stat, University of Calgary, Calgary, Canada): TBA
-
>15th Nov-Xu, Li
(Department of Math & Stat, University of Calgary, Calgary, Canada): Paper Review: TBA
'Investment timing under regime switching'

->1st Nov-Li, Hua (Department of Math & Stat, University of Calgary, Calgary, Canada): 'Application of fuzzy sets in finance'
->25th Oct-Swishchuk, Anatoliy
(Department of Math & Stat, University of Calgary, Calgary, Canada): : 'Pricing of variance swaps for stochastic volatilites with delay and jumps '

->18th Oct-Li,Hua: (Department of Math & Stat, University of Calgary, Calgary, Canada): Papers' Review:
1) 'Pricing and hedging derivative securities in markets with uncertain volatilites' by Avellaneda M., Levy A. and Paras A. (Appl. Math. Finance, 1995)
2) 'Uncertain parameters, an empirical stochastic volatility model and confidence limits' by Wilmott P. and Oztukel A. (1998)

->11th Oct-Risk Research Presentation (PRMIA Students Research Presentations, Bankers Hall, Calgary):
MacDonald, Scott (Direct Energy), Miao, Hong (Haskayne, U of C) and Orosi, Greg (Dept. of Math & Stat., U of C)

->4th Oct-Ware, Tony :
(Department of Math & Stat, University of Calgary, Calgary, Canada): 'Modelling Natural Gas Markets II'

->27th Sept-Badescu, Alexandru (Department of Math & Stat, University of Calgary, Calgary, Canada): 'Risk neutral measures for GARCH option pricing with normal variance-mean mixture examples'

->20th Sept-Ware, Tony (Department of Math & Stat, University of Calgary, Calgary, Canada) : 'Modelling Natural Gas Markets'

Summer 2007

->8th Aug-Zhao, Lu
(Department of Math & Stat, University of Calgary, Calgary, Canada):
'Modeling and Pricing of Variance and Volatility Swaps for Stochastic Volatilities with Jumps'

->18th Jul-Li, Hua  (Department of Math & Stat, University of Calgary, Calgary, Canada):
Papers'  review:
1)"Pricing European options based on the fuzzy pattern of Black-Scholes formula" Wu 2004,
and
2) "Using fuzzy sets theory and Black-Scholes formula to generate pricing boundaries of European options" Wu 2007.

->11th Jul-Ouyang, Yuyuan (Department of Math & Stat, University of Calgary, Calgary, Canada):
'European and Swing Option Pricing under mean-reverting jump diffusion models'

->20th Jun-Lyle, Matt (Department of Math & Stat, University of Calgary, Calgary, Canada):
1)
'A Brief Highlight of the "Mathematics of Electricity Supply & Pricing" Workshop in Surfers Paradise, Australia, 2007'

2)  'The Decomposition of Electricity Prices: A Master of Science Thesis Preview'
Winter 2007

->4th Apr-1) Ouyang, Yuyuan (Lance) (Department of Math & Stat, University of Calgary, Calgary, Canada): 'Swing Option Pricing under Jump-Diffusion Models'
2) Orosi, Greg
(Department of Math & Stat, University of Calgary, Calgary, Canada): 'Are Options Mispriced?'
3) Chan, Leunglung
(Department of Math & Stat, University of Calgary, Calgary, Canada): 'Option Pricing for GARCH Models with Markov Switching'
4) Miao, Hong
(Department of Math & Stat, University of Calgary, Calgary, Canada): 'VaR and CVaR: A Non-Normal Regime Switching Framework'
->28th Mar-1)  Xu, Li
(Department of Math & Stat, University of Calgary, Calgary, Canada): 'Pricing Variance Swaps for Stochastic Volatilities with Delay and Jumps'
2) Zhao, Lu
(Department of Math & Stat, University of Calgary, Calgary, Canada): 'Variance Swaps for Mean -Reverting Jump-Diffusion Models'
3) MacDonald, Scott
(Department of Math & Stat, University of Calgary, Calgary, Canada): 'Time Scale Decomposition of Economic Relationships Using Wavelet Analysis'

->21st Mar-Orosi, Greg (Department of Math & Stat, University of Calgary, Calgary, Canada): Book Review: 'Energy Derivatives' by Clewlow and Strickland, 2000.
Chapter 11:
'Credit Risk in Energy Markets'

->14th Mar-Xu, Li (Department of Math & Stat, University of Calgary, Calgary, Canada): Book Review: 'Energy Derivatives' by Clewlow and Strickland, 2000.
Chapter 10:
'Value at Risk'

->7th Mar-Zhao, Lu (Matthew) (Department of Math & Stat, University of Calgary, Calgary, Canada): Book Review: 'Energy Derivatives' by Clewlow and Strickland, 2000.
Chapter 9:
'Risk Management of Energy Derivatives'

->28th Feb-Lyle, Matt (Department of Math & Stat, University of Calgary, Calgary, Canada): Book Review: 'Energy Derivatives' by Clewlow and Strickland, 2000.
Chapter 8:
Forward Curve Models

->14th Feb-Ouyang, Yuyuan (Lance) (Department of Math & Stat, University of Calgary, Calgary, Canada): Book Review: 'Energy Derivatives' by Clewlow and Strickland, 2000.
Chapter 7: S
pot Price Models: Pricing Path Dependence and American Style Options
->7th Feb-Chan, Leunglung (Department of Math & Stat, University of Calgary, Calgary, Canada): 'Regime-Switching GARCH Models'

->31st Jan-Swishchuk, Anatoliy (Department of Math & Stat, University of Calgary, Calgary, Canada): Book Review: 'Energy Derivatives' by Clewlow and Strickland, 2000.
Chapter 6:
Spot Price Models and Pricing Standard Instruments
->24th Jan-Zhao, Lu (Matthew)  (Department of Math & Stat, University of Calgary, Calgary, Canada): Book Review: 'Energy Derivatives' by Clewlow and Strickland, 2000.
Chapter 5:
Energy Derivatives: Structures and Applications
->12th Jan (3:00pm-4:30pm)-Finance Research Seminar at Haskayne School of Business (U of C): Hamada, Mahmoud (Energy Australia): 'Real Options Theory and Electricity Forwards'

Fall 2006

->
5th Dec-Li, Xu  (
Department of Math & Stat, University of Calgary, Calgary, Canada): Book Review: 'Energy Derivatives' by Clewlow and Strickland, 2000.
Chapter 4: 'Energy Forward Curves'
->
28th Nov-Swishchuk, Anatoliy
(Department of Math & Stat, University of Calgary, Calgary, Canada): Book Review: 'Energy Derivatives' by Clewlow and Strickland, 2000.
Chapter 3: 'Volatility Estimation in Energy Markets'

->21st Nov-Ouyang, Yuyuan (Lance) (Department of Math & Stat, University of Calgary, Calgary, Canada): Book Review 'Energy Derivatives: Pricing and Risk Management' by Clewlow and Strickland,                      2000
'Understanding and Analysing Spot Pricing'

->7th Nov-Swishchuk, Anatoliy (Department of Math & Stat, University of Calgary, Calgary, Canada): Book Review 'Energy Derivatives: Pricing and Risk Management' by Clewlow and Strickland, 2000
'Introduction to Energy Derivatives and Fundamentals of Modelling and Pricing'

->31st Oct-Orosi, Greg (Department of Math & Stat, University of Calgary, Calgary, Canada) : 'Survey of Local Volatility Models'
Abstract:
In my talk I'll go over a survey of local volatility models (polynomial, spline, penalized spline). Also, I'll touch on the volatility smile problem and calibration of models to current option prices.
->24th Oct-Zhao, Lu
(Department of Math & Stat, University of Calgary, Calgary, Canada) : Paper's Review: Platen Eckhard "A Benchmark Approach to Finance", Math. Finance, vol 16, N1 (Jan
2006)

Abstract: This paper derives a unified framework for portfolio optimization, derivative pricing, financial modelling, and risk management.

->17th Oct-Swishchuk, Anatoliy (Department of Math & Stat, University of Calgary, Calgary, Canada) "Multi-Factor Stochastic Volatilities with Delay (SVD): Modelling and Pricing of Variance Swaps for
MFSVD (Part II)
"

Abstract:Variance swaps for financial markets with underlying asset and multi-factor stochastic volatilities with delay are modelled and priced in this talk. We obtain some analytical closed forms for the
expectations and variances of the realized continuously sampled variances for multi-factor stochastic volatilities with delay. As applications, we provide numerical examples using the S&P60 Canada Index
(1998-2002) to price variance swaps with delay for all these models.
->
10th Oct-Swishchuk, Anatoliy
(Department of Math & Stat, University of Calgary, Calgary, Canada) "Stochastic Volatilities with Delay (SVD): Modelling and Pricing of Variance Swaps for SVD (Part I)"
Abstract:     Modelling and pricing of variance swaps for financial markets with underlying asset and stochastic volatilities with delay are discussed in this talk. We found some analytical close forms for
expectation and variance of the realized continuously sampled variance for stochastic volatility with delay both in stationary regime and in general case. The key features of the stochastic volatility model with
delay are the following: i) continuous-time analogue of discrete-time GARCH model; ii) mean-reversion; iii) contains the same source of randomness as stock price; iv) market is complete; v) incorporates
the expectation of log-return. As applications, we provide two numerical examples using $S\&P60$ Canada Index (1998-2002) and $S\&P500$ Index (1990-1993) to price variance swaps with delay.

->3d Oct-1) Lyle, Matt (Department of Math & Stat, University of Calgary, Calgary, Canada) "Three electricity spot price models: Evidence from the PJM and Alberta markets (Part II)".
Abstract: We look at some simulation results based on three spot price models. The first is a random variable model i.e. non-SDE form; the second is a mean-reverting with jumps and "Laplacian" motion

model; the third is a mean-reverting with "many" jumps model.

2) Zhao, Lu (Matthew) (Department of Math & Stat, University of Calgary, Calgary, Canada)
Topic: Journals' Review:
i) Mathematical Finance (Jan/April/July/Oct 2006);
ii) Journal of Quantitative Finance (Aug/Oct/Dec 2005, Feb/April/June/Aug/Oct 2006).

->26th Sept-1) Lyle, Matt (Department of Math & Stat, University of Calgary, Calgary, Canada) "Cycle Detection and Removal in Electricity Prices" (Part 1)

Abstract: We use the Fast Fourier Transform (FFT) to help identify and remove seasonal or cyclical patterns within electricity data. This method allows for a robust and
accurate approximation of the cyclical components contained in the data, which in turn allows for a deeper study of the stochastic nature of electricity prices.
2) Ouyang, Yuyuan (Lance) (Department of Math & Stat, University of Calgary, Calgary, Canada)
Topic: Journals' Review:
i) Finance & Stochastics (Volume 10, Jan/Apr/Sep 2006)
ii) International Journal of Theoretical & Applied Finance (Volume 9,
Feb/Mar/May/Jun/Aug/Sep  2006)

Summer 2006

->7th July-Tony Ware  “Commodity Swaptions, Swing Contracts and Real Options in the Energy Industry ” (Chapter 5 of Helyette Geman's book "Commodities and commodity derivatives")

->23d June-Anatoliy Swishchuk “Spot and Forward Electgricity Market” (Chapter 11 of Helyette Geman's book "Commodities and commodity derivatives")

->9th June-Tony Ware “The Gas Market” (Chapter 10 of Helyette Geman's book "Commodities and commodity derivatives")

->2nd June-Anatoliy Swishchuk  “The Oil Market as a World Market” (Chapter 9 of Helyette Geman's book "Commodities and commodity derivatives")

->26th May-Alex David  “Agricaltural Commody Markets” and “The Structure of Metal Markets and Metal Prices” (Chapter 7-8 of Helyette Geman's book "Commodities and commodity derivatives")

->19th May- Tony Ware “Monte Carlo Simulations and Analytical Formulae for Asian, Barrier and Quanto Options ”(Chapter 6 of Helyette Geman's book "Commodities and commodity derivatives")

->12th May - Anatoliy Swishchuk. "Risk-Neutral Valuation of Plain-Vanilla Options" (Chapter 5 of Helyette Geman's book "Commodities and commodity derivatives").

->5th May - Traian A. Pirvu (Department of Mathematics, University of British Columbia, Vancouver, Canada). "Maximizing portfolio growth rate under risk constraints."

 Abstract: This work studies the problem of optimal investment subject to risk constraints: Value-at-Risk, Tail Value-at-Risk and Limited Expected Loss. We get closed-form solutions for this problem, and find that the optimal policy is a projection of the optimal portfolio of an unconstrained log agent (the Merton proportion) onto the constraint set, with respect to the inner product induced by the variance-covariance volatilities matrix of the risky assets. In the more complicated situation of constraint sets depending on the current wealth level, we maximize the growth rate of portfolio subject to these risk constraints. We extend the analysis to a market with random coefficients, which is not necessarily complete. We also perform a robust control analysis. We find that a trader subject to Value-at-Risk and Tail Value-at-Risk is allowed to incur some risk. A trader faced with the Limited Expected Loss constraint behaves more conservatively and does not exhibit the above behavior. This is a joint work with Steven Shreve and Gordan Zitkovic.

Winter semester 2006.

• 28th April - Tony Ware. "Option pricing: from stocks to commodities" (Chapter 4 of Helyette Geman's book "Commodities and commodity derivatives").
• 21st April - Anatoliy Swishchuk. "Stochastic modeling of commodity price processes" (Chapter 3 of Helyette Geman's book "Commodities and commodity derivatives").
• 7th April - Tony Ware. "Commodity and commodity derivatives" (Chapter 2 of Helyette Geman's book "Commodities and commodity derivatives").
• 31st March - Greg Orosi (Dept. of Math. & Stats., U. of C.). "Retrieving the implied volatility surface using splines."
 Abstract: Since its publication, the Black- Scholes option pricing formula has been widely used in the industry. However, there is much empirical evidence that the model is too simplistic because of the constant volatility assumption. In this talk I¡Çll describe an improvement over the Black-Scholes pricing framework that uses cubic splines to estimate the implied volatility surface from option prices. I'll also describe an optimization method called genetic algorithm and how this can be applied to the above problem.
• 24th March - Jennie La (Dept. of Math. & Stats., U. of C.). "Pricing of asian options."
 Abstract: Option pricing still remains an important problem for researchers, in particular, the options being considered may not have closed-form expressions, so it is difficult to price these options analytically. For this reason, numerical techniques such as simulations are often used for option pricing. This talk will introduce the type of simulation methods used, in particular, for pricing Asian options. In addition, this talk will show how simulation methods can be improved upon by introducing variance reduction techniques, specifically importance sampling. By applying variance reduction techniques to simulation methods, the price of the option can be accurately estimated and the computation time can be reduced.
• 17th March - Anatoliy Swishchuk. New series. "Fundamentals of commodity spot and futures markets: instruments, exchanges and strategies". (Chapter 1 of Helyette Geman's book "Commodities and commodity derivatives" (amazon.ca link, chapters.ca link). We will be reviewing selected chapters from this recent text in the coming weeks.
• 3rd March - Matt Davison (Associate Professor of Applied Mathematics, Faculty of Science Scholar, University of Western Ontario, ON, Canada), "Success and failure (in modelling) deregulated electricity markets."
 Abstract: Deregulated Energy Markets provide many opportunities and challenges - for mathematician and maker of public policy alike. In this talk I will describe the electricity markets work done in my group at UWO over the last six years, while placing this work in its broader economic and political context. The energy markets work we have done at UWO sits at the intersection of financial mathematics, operational research, and engineering. Our work has two main threads. We have developed a discrete - time model for spot electricity prices sitting between the old-fashioned "stack"-based models of regulated electricity markets and a fully econometric model appropriate to mature financial markets. I will describe the resulting "hybrid" model and some of its lessons. I will also describe our second, continuous-time, approach to energy markets. There we use classical dynamic programming tools to study the optimal control of electricity generating assets. In each case I will discuss obvious next steps as well as existing results. I will conclude my talk by discussing some crucial (though non-mathematical) aspects of electricity finance. These include lessons of Ontario's largely failed deregulation experiment not only for energy modelers but also for public policy wonks. I will also discuss some promising technological and policy developments which suggest that, for electricity deregulation, "better luck next time" might be more than just empty words.
• 17th February - Gordana Dmitrasinovic-Vidovic and Tony Ware (presenting), "Portfolio optimisation for log-normal and mean-reverting assets with respect to downside risk measures."
 Abstract: We consider managed portfolios of log- normal and mean-reverting assets, optimised with reference to various risk measures, but most notably quantile-based risk measures such as Capital-at- Risk and Value-at-Risk. These risk measures focus attention on the downside tail of the distribution of future portfolio values and are important for regulatory purposes. We give formulae for constructing optimal portfolios for specific choices of risk measure and explore some implications. Some of this work can be found in Asymptotic behaviour of mean-quantile efficient portfolios' (D-V & W), to appear in Finance and Stochastics.
• 10th February - Anatoliy Swishchuk, paper review "On the pricing and hedging of volatility derivatives" by S. Howison, A. Rafailidis and H. Rasmussen (2004).
• 3rd February - Anatoliy Swishchuk, paper review: "Parameter estimation in a stochastic drift hidden Markov model with a cap" by J. Hernandez, D. Suanders and L. Seco (2005).
• 27th January - Matthew Zhao, Variance and volatility swaps for markets with jumps.
• 20th January - Lance Ouyang, Mean-reverting models in finance with jumps. [Slides]
 Abstract: Mean-reverting models are important in finance, and are widely used in energy markets. I will give an presentation on mean-reverting models, mainly one-factor and two-factor Pilipovic models and their applications to obtaining explicit European option pricing formulae. A one-factor mean-reverting model with jumps will also be introduced.

Fall semester 2005.

• 6th December - Anatoliy Swishchuk, Girsanov's Theorem: from game theory to finance.
• 29th November - Tsung-lin Cheng, Statistical aspects of the GARCH model.
• 22nd November - Andrew Royal, Utility maximization in incomplete markets.
• 15th November - Hong Miao, A volatility model with Markov switching.
• 8th November - Anatoliy Swishchuk. Explicit option pricing formula for mean-reverting assets.
• 1st November - Tony Ware. Options with continuous exercise.
 Abstract: I will present an alternative formulation of the american option as a limiting case of continuously-exercisable options. This class of options can also be used to model gas-storage contracts and also includes swing options as a special case. I will show that the value of such an option may be found by solving a semilinear PDE (c.f. Benth et. al., Finance and Stochastics, 2003 for the american option case), and I will illustrate some numerical solutions of such equations.
• 25th October - Matthew Lu. Paper review: "A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets" by D. Heath, E. Platen and M. Schweizer (Math. Finance, vol. 11, N.4, 2001)
• 18th October - Anatoliy Swishchuk. Change of time method: applications in mathematical finance - I. [Slides]
 Abstract: I am going to give an introduction to the change of time method in the martingale and SDE settings and to show how it works for different kind of models and problems arising in mathematical finance. The first part contains applications to Black-Scholes model and Heston model. The second part will contain application to the mean-reverting model and option pricing.
• 11th October - Lance Ouyuang. Paper review: "Convergence of Monte-Carlo Simulations Involving the Mean-Reverting Square Root Process" by D. J. Higham and X. Mao (J. Computational Finance, 2005). [Slides]
• 4th October - Cody Hyndman. Forward-Backward Stochastic Differential Equations and the Cox-Ingersoll-Ross Model.
• 27th September - Yuyuan (Lance) Ouyuang and Zhao (Matthew) Lu will review recent issues of Finance and Stochastics, the Journal of Computational Finance, Mathematical Finance and the Journal of Quantitative Finance.
• 20th September - Leunglung Chan. Pricing Volatility Swaps Under Heston's Volatility Model with Regime Switching (this talk is based on joint paper with Robert Elliott and Tak Kuen Siu).

Spring-summer 2005
We are going to be reading selected chapters from Foundations of Modern Probability (Springer, 2002, 2nd ed.) by Olav Kallenberg.

Note that, beginning June 23rd, the seminars will start at 1.15pm.

21/7/05 Chapter 26. Semimartingales and General Stochastic Integration. Anatoliy Swishchuk presenting.

14/7/05 Chapter 24. Connections with PDEs and Potential Theory. Ka Chun Cheung presenting.

7/7/05 Chapter 23. One-Dimensional Stochastic Differential Equations and Diffusions. Anatoliy Swishchuk presenting.

30/6/05 Chapter 21. Stochastic Differential Equations and Martingale Problems. Ka Chun Cheung presenting.

23/6/05 Chapter 19. Feller processes and semigroups. Anatoliy Swishchuk presenting.

16/6/05 Chapter 18. Continuous martingales and Brownian motion. Ka Chun Cheung presenting.

9/6/05 Chapter 17. Stochastic integrals and quadratic variation. Anatoliy Swishchuk presenting.

2/6/05 Chapter 13. Gaussian Processes and Brownian Motion. Ka Chun Cheung presenting.

26/5/05 Chapter 12: Poisson and pure jump-type Markov processes. Anatoliy Swishchuk presenting.

18/5/05 Chapter 7: Martingales and optional times. Ka Chun Cheung presenting.

Winter 2005

21/4/05 Miro Powojowski (TD Securities, Calgary, AB, Canada) How to calculate the vega without working too hard.

 Abstract: I propose a simple method for computing the vega for a fairly wide class of models including jump-diffusion.

14/4/05 Anatoliy Swishchuk. Yet one more derivation of Black-Scholes formula: change of time method.

 Abstract: I am going to present yet one more derivation of the well-known Black-Scholes formula using a change-of-time method.

7/4/05 Robert Elliott (Haskayne School of Business, U of C). Cutting the hedge.

 Abstract: We shall describe a short empirical way of calculating the delta.

31/3/05 Anatoliy Swishchuk. Mean-Reverting Models in Financial and Energy Markets. [2pm, MS431.]

 Abstract: We are going to introduce some mean-reverting models (asset prices or their volatilities tend over time to return to some long-term mean) in financial and energy markets. For these models, we present several recent results on option pricing formula and on volatility and variance swaps.

24/3/05 Hua Li (Department of Mathematics and Statistics, UofC). Numerical Methods for Parabolic Integro-Differential Equations (PIDEs).

 Abstract: Parabolic integro-differential equations(PIDEs) have been used in option pricing when the underlying price process has jumps. In this talk, we introduce various numerical methods for solving them that have appeared in the literature, and summarize the corresponding advantages and drawbacks. We will conclude that the wavelet-Galerkin (or wavelet-Petrov- Galerkin) method is preferable to finite-difference and finite- element approaches.

17/3/05 Cheung, Ka Chun (Department of Mathematics and Statistics, UofC). Ordering optimal proportions in the asset allocation problem with dependent default risks.

10/3/05 Anatoliy Swishchuk. Explicit Option Pricing Formula for Mean-Reverting Asset.

 Abstract: Unlike stock price, some commodity prices (i.e., oil and gas) exibit mean-reversion, i.e., they tend over time to return to some long-term mean. We consider a risky asset following a mean-reverting stochastic process S(t) described by the following stochastic differential equation dS(t)=a(L-S(t))dt+\sigma S(t)dW(t), where W is a standard Wiener process, \sigma>0 is the volatility, constant L is callled the 'long-term mean' of the process, to which it reverts over time, and a>0 measures the 'strength' of mean reversion. Using change of time method we find the explicit solution to this equation and using this solution we are able to find the explicit option pricing formula. We are going to apply our solution to the calculation of the values of a European call option on the price of a daily natural gas contract, using futures prices for the AECO Natural Gas Index for the period 1 May 1998 to 30 April 1999.

3/3/05 Leung Leung Chan. Option Pricing and Esscher Transform under Regime Switching.

3/2/05 Anatoliy Swishchuk. Levy Processes-From Probability to Finance.

27/1/05 Graham Weir. The Valuation of Petroleum Lease Contracts as Real Options.

Fall 2004

16/12/04 Gordon Sick. Calibrating mean-reverting models to NYMEX oil and gas futures and options.

9/12/04 Guanghui Quan, Nine Ways to implement the binomial method for option valuation in MATLAB (based on Higham's SIAM review paper).

2/12/04 Gordana Dmitrasinovic-Vidovic, Portfolio optimisation under downside risk measures.

25/11/04

18/11/04 Gergely Orosi: Neural networks in finance.

11/11/04 Rememberance day, no meeting.

4/11/04 (1.30pm) Finance Research Seminar. Matt Spiegel, Improved forecasting of mutual fund alphas and betas. 1.30pm, SH215.

28/10/04 Anatoliy Swishchuk: Financial Markets with Stochastic Volatilities.

21/10/04 Finance Research Seminar. Lisa Kramer: Investing Confidence in the Ex Ante Equity Premium: A New Methodology and a Narrower Range of Estimates.

14/10/04 Lei Xiong: Calibration of energy price processes using jump-diffusion models.

7/10/04 Tony Ware: Welcome to the Mathematical and Computational Finance Laboratory.