AMAT 581/681 (Fall 2015)
"Stochastic Calculus for Finance"
Course Outline
Instructor:
Anatoliy Swishchuk
E-mail: aswish@ucalgary.ca
Office: MS552
Tel.: (403) 220-3274
Office Hours:
TuTh:11:00am-12:00pm

Place:  MS205

Lectures Schedule

Tuesday
Thursday
9:30am-10:45am (75 minutes)
 
9:30am-10:45am (75 minutes)
 
Syllabus:
1) Stochastic Calculus and the Dynamics of Asset Prices
2) Martingale Theory and Risk-Neutral Valuation
3) Interest Rate Models
4) Energy and Commodity Markets
6) Value-at-Risk and Risk Management
7) Levy Processes in Finance

 Important Class Dates:
First Class: Tuesday, September 8, 2015, 9:30am
Last day of class: Tue, December 8, 2015
A#1-5 due dates: Sep22, Oct6, Oct20, Nov3, Nov17
Project due date: Dec 8, 2015
Recommended texts: 
          Lecture Notes    
Course Information Sheet
Course Web Page:
The current official syllabus for this course is available in the wall pockets across from MS 476 and
on the webpage at www.math.ucalgary.ca Course Listing-Undergraduate.
There is also a web page for this course which contains the course outline, tentative course schedule,  grading scheme, important class dates, etc.
Announcements made in class will be posted there (see end of this web-page). The address of this web page is: http://www.math.ucalgary.ca/~aswish/amat581_681Fall2015.html/

Class work:
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):

Assignments, Project
Due Dates for Assignments and Project
Assignmnmets: 50%
A1:Sept22; A2:Oct6; A3:Oct20; A4:Nov3; A5:Nov17
Project: 50 %
Dec 8, 2015 (pdf-file sent by e-mail)


Tentative Lectures Schedule for AMAT 581/681
Month
Days
Tuesday/Thursday
Sept
8/10
Lec1/2: Course Outline. Introduction to Options and Futures. Probability Spaces, Sigma Algebras, Stopping Times.
Sept
15/17
Lec3/4: Conditional Probabilities and Expectations: Definitions, Basic Properties. Discrete-Time Martingales, Sub- and Supermartingales: Definition and Examples. Martingale Transforms and Representation Theorem.
Sept
22/24
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.
Sept/Oct
29/1
Lec7/8: Continuous-Time Martingales, Sub- and Supermartingales: Definition and Examples. Wiener Process and Poisson Process.  Stochastic Integration: Ito Integral.
Oct
6/8
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.
Oct
13/15
Lec11/12:  Girsanov Theorem. Continuous (B,S)-Security Markets: Definitions and Basic Properties.
Oct
20/22
Lec13/14: Risk-Neutral Valuation, Black-Scholes Formula, Call-Put Parity, The Greeks.
Oct
27/29
Lec15/16: Stopping Times, Wald's Identities, American Options.
Nov
3/5
Lec17/18: Interest Rate Models I:  Modelling, Yield Curves, Bond Option Prices. The Ornstein-Uhlenbeck and Vasicek Models.
Nov
11-15
Reading Days (no classes)
Nov
10/17
Lec19/20: Interest Rate Models II: The Cox-Ingersoll-Ross , Hull-White and Heath-Jarrow-Morton Models.
Nov
19/24
Lec21/22: Energy and Commodity Markets: Definitions and Examples, Modelling,  Main Statistical Instruments I (pdf).
(Geman Book: Intro)
Nov/Dec
26/1
Lec23/24: Stochastic Modeling of Energy and Commodity Price Processes.
(Geman Book: Chapter 3)
Change of Time Method in Finance   Quantitative, Energy and Environmental Finance
Dec
3/8
Lec25/26: Value at Risk and Risk Management. Levy Processes in Finance.

Announcements: 
Assignments
5) Assignment #5: Due-November 17, 2015 (in-class)
4) Assignment #4: Due-November 3, 2015 (in-class)
3) Assignment #3: Due-October 20, 2015 (in-class)
2) Assignment #2: Due-October 6, 2015 (in class)
1) Assignment #1: Due-September 22, 2015 (in-class)

Projects (pdf-file sent by e-mail): Due-Tuesday, December 8, 2015

 
This page was updated on December 22, 2015.