Ects : 6

Compétence à acquérir :

The lecture starts with discrete time models which can be viewed as a proxy for continuous settings. We then develop on the theory of continuous time models. We start with a general Itô-type framework and then specialize to different situations: Markovian models, constant volatility models, local and stochastic volatility models.For each of them, we discuss their calibration, and the valuation and the hedging of different types of options : plain Vanilla and barrier options, contracts on future, American options, options on foreign markets, options on realized variance, etc.

Compétence à acquérir :

The lecture starts with discrete time models which can be viewed as a proxy for continuous settings. We then develop on the theory of continuous time models. We start with a general Itô-type framework and then specialize to different situations: Markovian models, constant volatility models, local and stochastic volatility models.For each of them, we discuss their calibration, and the valuation and the hedging of different types of options : plain Vanilla and barrier options, contracts on future, American options, options on foreign markets, options on realized variance, etc.

Description du contenu de l'enseignement :

Advanced derivative pricing and stochastic calculus.

This course requires that the students have validated the course "Finance in continuous time". Its gives more insights into the theory of derivative asset pricing as well as the main models and techniques used in practice.