PAUL GASSIAT - Maître de Conférence, Université Paris-Dauphine
The aim of this lecture is to present the theory of derivative asset pricing as well as the main models and techniques used in practice. 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, American options, options on realized variance,...).
Les étudiants doivent avoir validé les cours de Produits dérivés et d'Evaluation de dérivés et Calcul stochastique 1
I. Discrete time modelling
I.1. Financial assets
I.2. The absence of arbitrage
I.3. Pricing and hedging of European options
I.4. Pricing and hedging of American options
II. Continuous time modelling
II.1. Financial assets as Itô processes
II.2. The Black-Scholes model
II.3. Markovian models in complete markets
II.4. Local volatility models
II.5. Stochastic volatility models
Bouchard B. et Chassagneux J.F., Fundamentals and advanced Techniques in derivatives hedging, Springer, 2016.
Lamberton D. et B. Lapeyre, Introduction au calcul stochastique appliqué à la finance, Ellipses, Paris, 1999.