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--- en:ddefimafi2022 [2022/05/05 16:41] – [Brief description] cpouet
+++ en:ddefimafi2022 [2022/07/04 15:30] – [Course metadata] cpouet
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+=====Course unit: Mathematical finance =====
+** <color red> Beware! Under construction. </color> **
+==== Course metadata ====
+  * Title in French: Mathématiques financières
+  * Course code: tba
+  * ECTS credits: 8
+  * Type: specialized course
+  * Semester 10 (Spring)
+  * Teaching period: Mid-February to Mid-April
+  * Teaching hours: 100h
+  * Language of instruction: English
+  * Coordinator: tba
+  * Instructor(s): Sébastien Darses (AMU), Ismaïl Akil (Bank of America Merrill Lynch), Abderrahim Ben Jazia (RSM Paris)
+  * //Last update 04/07/2022 by C. Pouet//
+==== Brief description ====
+The aim of the course is to provide students with mathematical methods that allow valuating financial assets. Several instructors are Centrale Marseille alumni.
+This course unit is divided into four parts:
+  * ** Stochastic calculus and introduction to the Black-Scholes model ** (tba hours) taught by Sébastien Darses.
+  * ** Volatility models ** (tba hours) taught by Ismaïl Akil.
+  * ** Interest rate models ** (tba hours) taught by Abderrahim Ben Jazia.
+  * ** Data Project: modeling and validation ** (tba hours) taught by tba.
+==== 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
+=== Data Project:  modeling and validation ===
+tba
+==== Bibliography ====
+You can 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.