Teaching

Here is a list of the courses that I currently teach. Part of my teaching material can be downloaded below.

- Stochastic processes in continuous time

1. Basics about stochastic process in continuous time

1.1 Definition and notion of filtration

1.2 Stopping times

1.3 Measurability and classes of stochastic processes

1.4 Markov property

1.5 Martingales

2. Introduction to Brownian motion

2.1 Existence of Brownian motion as the limit of a symmetric random walk in discrete time

2.2 Definition of Brownian motion

2.3 Nowhere differentiability of Brownian paths

2.4 Infinite variation and positive quadratic variation

2.5 Some functions of Brownian motion

2.6 Brownian martingales

2.7 Boundary crossing distributions of Brownian motion

2.8 Multidimensional Brownian motion

3. Stochastic differentiation

3.1 Ito’s formula

3.2 Differentiation of functions of several correlated Ito processes

4. Stochastic integration

4.1 Introduction to the stochastic integral

4.2 Construction of the Ito integral in discrete time

4.3 Extension of the Ito integral in continuous time

4.4 Basic techniques for solving SDEs

5. Change of probability measure

5.1 Valuation of contingent claims

5.2 Proof of Girsanov’s theorem and extension to multidimensional version

5.3 Application of Girsanov’s theorem to boundary crossing problems

- Stochastic modeling applied to finance

This is a graduate course taught at the University of Cergy-Pontoise for the students from the Master in Quantitative Finance and from the Master in Applied Mathematics.

Syllabus :

- Laplace and Fourier transforms

- Linear 2nd order partial differential equations

- Brownian motion and diffusion processes

- Stochastic integration

- Valuation of options on equity and foreign exchange in a complete market model

- Interest rate modeling

- Jump processes

- Stochastic simulation in finance

This is a graduate course taught at the University of Cergy-Pontoise for the students from the Master in Quantitative Finance and from the Master in Applied Mathematics.

Syllabus :

- Random number generators

- Sampling methods

- Brownian bridge

- Control variates

- Simulation of jump processes

- Exotic Options and Structured Products

This is a course taught at the University of Cergy-Pontoise for the students from the Master in Quantitative Finance.

Syllabus :

- Dynamic and static hedging

- Smiles and skews

- Examples of structuring through combinations of bonds and options