Valuation of financial assets and arbitrage

Crédit : 6 ECTS
Langue du cours : anglais

Volume horaire

• CM : 30 h
• Volume horaire global (hors stage) : 30 h

Compétences à acquérir

The lecture starts with discrete time models which can be viewed as a proxy for continuous settings, and for which we present in detail the theory of arbitrage pricing. 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, local and stochastic volatility models. For each of them, we discuss the valuation and the hedging of different types of options : plain Vanilla and barrier options, American options, options on realized variance, etc. Finally, we present several specific volatility models (Heston, CEV, SABR,...) and discuss their specificities.

Description du contenu de l'enseignement

Course outline: I. Discrete time modelling I.1. Financial assets I.2. The No arbitrage condition and martingale measures (FTAP) I.3. Pricing and hedging of European options; market completeness and 2nd FTAP I.4. Pricing and hedging of American options (in a complete market) II. Continuous time modelling II.1. Financial assets as Itô processes : general theory II.2. Markovian models : PDE pricing, delta-hedging (European options, barrier options, American options) II.3. Local volatility models and Dupire's formula II.4. Stochastic volatility models : how to deal with market incompleteness; (semi-)static hedging; specific models and their properties

Bibliographie, lectures recommandées

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.

Enseignant responsable

JULIEN CLAISSE

Enseignant responsable

PHILIPPE BERGAULT