*This information is indicative and can be subject to change.*

Malliavin calculus and Monte Carlo methods

Teacher: Christophe Chorro

E-mail: christophe.chorro@univ-paris1.fr

ECTS: 2.5

Evaluation: Numerical Project

Previsional Place and time: MSE, Wednesday from 13h to 16h

Prerequisites: Basic functional analysis, Probability theory, Stochastic calculus 1 and 2.

Aim of the course: The aim of this course is to introduce the elementary aspects of the so-called stochastic calculus of variations (also called Malliavin calculus) on the Wiener space in particular for financial applications. We will define the main operators of the theory (derivative and Skorohod operators) in order to:

• Prove the Clark-Ocone formula and see the relation with hedging problems

• Use the integration by parts formula to compute efficiently the Greeks by Monte Carlo methods

Syllabus:

0) Presentation of the problem

0.1) Monte Carlo Methods

0.2) Pricing and Hedging in finance

0.3) Greeks computation

1) The derivative operator

2) The Skorohod integral

3) Computation of Greeks

References:

Course material is available here.

• D. Nualart : The Malliavin Calculus and Related Topics, Springer-Verlag, seconde édition,

2006.

• E. Fournier and al: Applications of Malliavin calculus to Monte-Carlo methods in finance,

Finance and Stochastics, 3, 391-412, 1999.

• B. Oksendal: An Introduction to Malliavin Calculus with Applications to Economics, 1996.