|9:30am-10:45am (75 minutes)
9:30am-10:45am (75 minutes)
In-class lectures with typical examples (lecture notes will be posted on the webpage in the form of pdf-files);
your computer must have an Adobe Acrobat reader (for free downloading see www.adobe.com).
Grading scheme (Course Evaluation):
||Due Dates for Assignments and Project
||A1:Sept27; A2:Oct11; A3:Oct25; A4: Nov8; A5:Nov29
|Project: 50 %
||Dec 8, 2016 (pdf-file sent by e-mail)
||Lec1/2: Course Outline. Intro to
Probability: Probability Spaces, Sigma-Algebras, Stopping
Times, LLN, CLT.
||Lec3/4: Conditional Probabilities and Expectations: Definitions, Basic Properties. Discrete-Time Martingales, Sub- and Supermartingales: Definition and Examples. Martingale Transforms and Representation Theorem.|
||Lec5/6: Discrete (B,S)-Security Markets:
Definitions and Basic Properties. Risk-Neutral Valuation:
Cox-Ross-Rubinstein Formula. General (B,S)-Security
Markets: Definition, Basic Properties. (A#1
due: Sept 27)
||Lec7/8: Continuous-Time Martingales, Sub-
and Supermartingales: Definition and Examples. Wiener
Process and Poisson Process. Stochastic Integration:
||Lec9/10: Stochastic Differential Equations and Ito Formula. Integration by Parts Formula. Martingale Representation Theorem in Continuous Time (Brownian Representation) and Levy Characterization of Brownian Motion. (A#2 due: Oct 11)|
||Lec11/12: Girsanov Theorem.
Continuous (B,S)-Security Markets: Definitions and Basic
||Lec13/14: Risk-Neutral Valuation, Black-Scholes Formula, Call-Put Parity, The Greeks. (A#3 due: Oct 25)|
Stopping Times, Wald's Identities, American Options.
||Lec17/18: Interest Rate Models I: Modelling, Yield Curves, Bond Option Prices. The Ornstein-Uhlenbeck and Vasicek Models. (A#4 due: Nov 8) Nov 10: Reading Days (no classes)|
||Lec19/20: Interest Rate Models II: The Cox-Ingersoll-Ross , Hull-White and Heath-Jarrow-Morton Models.|
Energy and Commodity Markets: Definitions and
Examples, Modelling, Main Statistical Instruments I.
(Geman Book: Intro)
Modeling of Energy and Commodity Price Processes.
(Geman Book: Chapter 3)
(A#5 due: Nov 29)
||Lec25/26: Value at Risk and Risk
Management. Levy Processes in Finance.
(Project due: Dec 8)
5) Assignment #5: Due-November 29, 2016 (in-class)
4) Assignment #4: Due-November 8, 2016 (in-class)
3) Assignment #3: Due-October 25, 2016 (in-class)
2) Assignment #2: Due-October 11, 2016 (in class)
1) Assignment #1: Due-September 27, 2016 (in-class)
Projects (pdf-file sent by e-mail): Due-Thursday, December 8, 2016