| Wednesday |
Friday |
| 13-14:15
(75 minutes) |
11am-12:15 (75 minutes) |
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:Jan
27; A2:Feb 10; A3:Feb 27; A4:Mar 10; A5:Mar 24 (in-class) |
| Project:
50 % |
April
12, 2006 (in-class) |
| Month |
Days |
Wednesday/Friday |
| Jan |
11/13 |
Lec1/2:
Course Outline.
Introduction to Options and Futures. Probability Spaces, Sigma
Algebras, Stopping Times. |
| Jan |
18/20 |
Lec3/4: Conditional Probabilities and Expectations: Definitions, Basic Properties. Discrete-Time Martingales, Sub- and Supermartingales: Definition and Examples. Martingale Transforms and Representation Theorem. |
| Jan |
25/27 |
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. |
| Feb |
1/3 |
Lec7/8: Continuous-Tine Martingales, Sub- and Supermartingales: Definition and Examples. Wiener Process and Poisson Process. Stochastic Integration: Ito Integral. |
| Feb |
8/10 |
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. |
| Feb |
15/17 |
Lec11/12: Girsanov Theorem. Continuous (B,S)-Security Markets: Definitions and Basic Properties. |
| Feb |
22/24 |
Reading
Week (no classes) |
| Mar |
1/3 |
Lec13/14: Risk-Neutral Valuation,Black-Scholes Formula, Call-Put Parity, The Greeks. |
| Mar |
8/10 |
Lec15/16:
Stopping Times, Wald's Identities, American Options. |
| Mar |
15/17 |
Lec17/18:
Interest Rate Models I: Modelling, Yield Curves, Bond Option
Prices. The
Ornstein-Uhlenbeck and Vasicek Models. |
| Mar |
22/24 |
Lec19/20:
Interest Rate Models
II:
The
Cox-Ingersoll-Ross , Hull-White and Heath-Jarrow-Morton Models. |
| Mar |
29/31 |
Lec21:
Commodity Markets:
Introduction (ppt). Lec22: Energy and Commodity Markets: Definitions and Examples, Modelling, Main Statistical Instruments.I (pdf). |
| Apr |
5/7 |
Lec23/24:
Stochastic Modeling of Energy and Commodity Price Processes. |
| Apr |
12 |
Lec25:
Value-at-Risk:
Definition and Examples, Basic Calculations. Risk Management. |
| 5)
Assignment #5: Due-March 24, 2006 (in-class) 4) Assignment #4: Due-March 10, 2006 (in-class) 3) Assignment #3: Due-February 27, 2006 (Drop-Off Box, MS552) 2) Assignment #2: Due-February 10, 2006 (in-class) 1) Assignment #1: Due-January 27, 2006 (in-class) |