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en:ddefimatfi [2021/03/23 12:00] cpoueten:ddefimafi [2021/08/27 10:19] (Version actuelle) – [Course metadata] cpouet
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 +=====Course unit: Mathematical finance =====
 +==== Course metadata ====
 +  * 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//
  
 +==== Brief description ====
 +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.
 +
 +==== Learning outcomes ====
 +
 +  * 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
 +
 +
 +==== Course content ====
 +
 +
 +=== Stochastic calculus and introduction to the Black-Scholes model===
 +
 +  - Gaussian variable and stochastic processes
 +  - Brownian motions
 +  - Stochastic integration and semi-martingales
 +  - Stochastic differential equations
 +  - Parabolic partial differential equations and semigroups
 +  - Measure change and Girsanov theorem
 +  - Introduction to financial mathematics
 +
 +=== Volatility models====
 +  - Elementary financial mathematics notions
 +  - PDE: Black Scholes and risk neutral measure
 +  - Dupire’s local volatility: advantages and drawbacks
 +  - Stochastic volatility (Heston and SABR)
 +  - Tutorial: discretization of the Heston’s model
 +
 +=== Interest rate models===
 +  - A Mathematical Toolkit
 +  - Interest rates, swaps and options
 +  - One-factor Short-Rates Models
 +  - Two-factor Short-Rates Models
 +  - The Health-Jarrow-Morton (HJM) Model
 +  - The change of numeraire
 +  - Derivatives Pricing under the Libor Market Model
 +
 +==== Bibliography ====
 +Check the availability of the books below at [[https://documentation.centrale-marseille.fr/|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.