en:ddefimafi

• Title in French: Mathématiques financières
• Course code: tba
• ECTS credits: 3
• Teaching hours: 72h
• Type: specialized course
• Language of instruction: English
• Coordinator: tba
• Instructor(s): Sébastien Darses (AMU), Ismaïl Akil (tba), Abderrahim Ben Jazia (RSM Paris)
• Last update 27/08/2021 by C. Pouet

The aim of the course is to provide students with mathematical methods that allow valuating financial assets.

This course unit is divided into three parts:

• Stochastic calculus and introduction to the Black-Scholes model (24 hours) taught by Sébastien Darses.
• Volatility models (24 hours) taught by Ismaïl Akil.
• Interest rate models (24 hours) taught by Abderrahim Ben Jazia.
• Understand stochastic calculus and know how to apply its main results
• Know how to apply stochastic methods to price financial products
• Understand the mathematical contexts under which the classical financial mathematics models hold
• Know and understand the relevance and limits of financial mathematics models
• Understand the impact of volatility on the profit and losses of a hedged position
• Know how to build numerical methods for pricing financial products

#### Stochastic calculus and introduction to the Black-Scholes model

1. Gaussian variable and stochastic processes
2. Brownian motions
3. Stochastic integration and semi-martingales
4. Stochastic differential equations
5. Parabolic partial differential equations and semigroups
6. Measure change and Girsanov theorem
7. Introduction to financial mathematics

#### Volatility models

1. Elementary financial mathematics notions
2. PDE: Black Scholes and risk neutral measure
3. Dupire’s local volatility: advantages and drawbacks
4. Stochastic volatility (Heston and SABR)
5. Tutorial: discretization of the Heston’s model

#### Interest rate models

1. A Mathematical Toolkit
2. Interest rates, swaps and options
3. One-factor Short-Rates Models
4. Two-factor Short-Rates Models
5. The Health-Jarrow-Morton (HJM) Model
6. The change of numeraire
7. Derivatives Pricing under the Libor Market Model

Check the availability of the books below at Centrale Marseille library. - Stochastic calculus

• Evans, L. (2010). An Introduction to Stochastic Differential Equation. American Mathematical Society.
• Le Gall, J.-F. (2006). Intégration, Probabilités et Processus Aléatoires. Ecole Normale Supérieure de Paris

- Volatility models

• El Karoui, N. (2004) Couverture des risques dans les marchés financiers. Ecole Polytechnique

- Interest rate models

• Brigo, D., & Mercurio, F. (2007). Interest rate models-theory and practice: with smile, inflation and credit. Springer Science & Business Media
• Privault, N. (2012). An elementary introduction to stochastic interest rate modeling. World Scientific.
• en/ddefimafi.txt
• Dernière modification: 2021/08/27 08:19
• par cpouet