11am-12:15 (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).
scheme (Course Evaluation):
Dates for Assignments and Project
27; A2:Feb 10; A3:Feb 27; A4:Mar 10; A5:Mar 24 (in-class)
12, 2006 (in-class)
Introduction to Options and Futures. Probability Spaces, Sigma
Algebras, Stopping Times.
||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.|
||Lec7/8: Continuous-Tine Martingales, Sub- and Supermartingales: Definition and Examples. Wiener Process and Poisson Process. Stochastic Integration: Ito Integral.|
Equations and Ito Formula. Integration by Parts
Formula. Martingale Representation Theorem in Continuous Time (Brownian
Representation) and Levy Characterization of
||Lec11/12: Girsanov Theorem. Continuous (B,S)-Security Markets: Definitions and Basic Properties.|
Week (no classes)
||Lec13/14: Risk-Neutral Valuation,Black-Scholes Formula, Call-Put Parity, The Greeks.|
Stopping Times, Wald's Identities, American Options.
Interest Rate Models I: Modelling, Yield Curves, Bond Option
Ornstein-Uhlenbeck and Vasicek Models.
Interest Rate Models
Cox-Ingersoll-Ross , Hull-White and Heath-Jarrow-Morton Models.
Lec22: Energy and Commodity Markets: Definitions and Examples, Modelling, Main Statistical Instruments.I (pdf).
Stochastic Modeling of Energy and Commodity Price Processes.
Definition and Examples, Basic Calculations. Risk Management.
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)