ST330 Stochastic and Actuarial Methods in Finance

Michaelmas term 2011 and Lent term 2012

Page contents

• Course contents
• Course materials

The course is made up of 40 hours of lectures and 20 hours seminars. For the Michaelmas term:

• Lectures: Tuesday 11:00-13:00 in STC.75
• Seminars: Wednesday 9:00-10:00 in STC.75

• Lectures: Monday 9:00-11:00 in CLM.6.02
• Seminars: Monday 11:00-12:00 in CLM.6.02

Course contents

1. Choice under Uncertainty :

   • Utility theory: Utility functions, expected utility theorem, certainty equivalent, non-satiation principle, risk-aversion.
   • Stochastic dominance.
   • Risk measures.

2. Portfolio Theory :

   • Mean-variance paradigm: opportunity set, efficient portfolios.
   • Markovitz model.
   • Capital Asset Pricing Model: assumptions, efficient frontier, pricing formula.
   • Arbitrage Pricing Theory: factor models.
   • Efficient Market Hypothesis.

3. Introduction to financial derivatives :

   • General introduction.
   • Options and other derivatives.
   • Some preliminary remarks on derivatives pricing.

4. Discrete-time models of financial markets :

   • The Cox-Ross-Rubinstein model.
   • General presentation and fundamental notions: no-arbitrage, completeness...

5. Continuous-time models of financial markets :

   • Some recalls on stochastic calculus.
   • General presentation and fundamental notions: no-arbitrage, completeness...
   • The Black and Scholes model: assumptions, fundamental PDE, BS formula and its extensions.

6. Interest rate modeling :

   • Basic fixed income objects.
   • Short-rate models.
   • Modeling the forward rate dynamics: HJM methodology.

7. Introduction to credit risk

Course materials

Exercises and various documents (see Moodle)

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