Ects : 3

Enseignant responsable :

• TETE KAIZA AMOUH

Volume horaire : 21

Description du contenu de l'enseignement :

The course bears on the modeling and numerical analysis of financial derivatives. The objectives are:

• Understanding the financial meaning of the related mathematics: model parameters, implied volatility, Greeks.
• Learning how to derive a pricing equation based on the probabilistic formulation of a model, possibly with stochastic volatility and/or jumps,
• Learning how to implement a theta-scheme of finite differences or a tree pricing method,
• Learning simulation Monte Carlo pricing and Greeking methods: basic principles and variance reduction techniques, first in a set-up of random variables or vectors, then in a dynamic set-up of stochastic processes.

Course outline: 1) Motivating examples: Black-Scholes and Dupire model, Realized volatility vs Implied volatility vs Local volatility, 2) Derivation of the Pricing Equations in various models, 3) Deterministic Pricing Schemes: Finite Differences methods and Tree Methods 4) Simulation Pricing Schemes: simulation of random variables and stochastic processes, Pseudo Monte Carlo versus Quasi Monte Carlo, variance reduction techniques

Pré-requis obligatoires :

Students must be enrolled in courses Derivative Pricing and Stochastic Calculus 2 and C++ Programming and must have past Financial Derivatives and Derivative Pricing and Stochastic Calculus 1

Coefficient : 1.5

Compétence à acquérir :

Master the modelling and numerical analysis of financial derivatives

Mode de contrôle des connaissances :

Project (in teams of two to three students)  

Bibliographie, lectures recommandées

Crépey S., Computational Finance Lecture Notes, 2009 edition, 188 pages, available on www.maths.univ-evry.fr/crepey Lamberton D. and Lapeyre P., Introduction to Stochastic Calculus Applied to Finance. Chapman & Hall, 2nd revised edition, 2007. Shreve S., Stochastic Calculus for Finance II, Springer Finance, 2008. Hull J., Options, Futures, and Other Derivative Securities, Prentice-Hall, 7th edition, 2009.