Derivative products are an important way for the investors to protect themselves against market risks in the future. The stochastic calculus has enabled the development of this industry. In this course, we will describe the financial products and the methods used by the market to price and hedge them. First, we explain the main concepts of option pricing in the simple framework of discrete-time financial markets and finite probability spaces. Next, after introducing the necessary tools of stochastic calculus, we review the Black-Scholes option pricing theory and the basics of optimal asset allocation in continuous time.

List of topics :
1. Discrete-time financial markets: no-arbitrage, market completeness; optimal portfolio choice.
2. The Cox-Ross-Rubinstein model (binomial tree) and its continuous-time limit.
3. Brownian motion, stochastic integration with respect to Brownian motion and Itô’s formula.
4. Continuous-time financial markets and the Black-Scholes model.
5. Optimal asset allocation in continuous-time financial markets; Merton’s portfolio problem.

References:
Peter Tankov, Nizar Touzi, “No-arbitrage theory for derivatives pricing”, poly Ecole Polytechnique
Darrel Duffie, “Dynamic asset pricing theory”, Princeton University Press (2001)

Only PA QEF

Modalités d'évaluation : Un examen écrit.

Dernière mise à jour : vendredi 23 mars 2012