ST409 Stochastic Processes

Lent term 2003

Page contents

• Course contents
• Course materials

The course is made up of 20 hours of lectures and 10 hours seminars.

• Lectures: Monday 16:00-18:00 in D106
• Seminars: Wednesday 12:00-13:00 in D106

Course contents

1. Some recalls on Probability Theory :

   • Probability space, probability measure, random variables.
   • Discrete and continuous distributions..
   • Cumulative distribution function, density, Laplace transform.

2. Stochastic Processes :

   • Definitions
   • Discrete and continuous martingales.
   • Brownian motion and its main properties.
   • Stochastic calculus: Ito's formula, Girsanov's theorem, Feynman-Kac formula...
   • An introduction to SDE.

3. Some financial applications :

   • Discrete-time models of financial markets: general presentation and fundamental notions (no-arbitrage, completeness...).
   • Continuous-time models of financial markets: general presentation and fundamental notions (no-arbitrage, completeness...).
   • The Black and Scholes model: assumptions, fundamental PDE, BS formula and its extensions.

4. Further applications :

   • Interest rate modelling: short-rate models, modelling the forward rate dynamics (HJM methodology).

Course materials

Exercises (See the Public folders)

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