The purpose of this course is to present the basics of probability theory and continuous time processes, allowing for a rigorous understanding of the standard dynamic stock models. Due to the motivations of the course, the mathematical concepts will be taught, considering concrete financial applications.
After a review of basic probability notions, the course will focus on the rigorous mathematical definition of arbitrage opportunities, leading to basic financial derivative valuation techniques. After a study of option pricing in multiperiod binomial models, we introduce stochastic calculus tools such as Brownian motion, stochastic integral and Ito formula. With these instruments, a complete study of the classical Black Scholes model will be performed: option valuation, PDE price characterization and Greeks computation. If time permits, the last chapter will deal with Monte Carlo simulations and practical calibration and estimation methods for the coefficients of the Black Scholes model.
A support class is offered to M1-level students. The purpose of this support course is to illustrate and apply the notion studied in the ‘Derivatives pricing and stochastic calculus 1’ course. After a quick review of the key concepts presented in class, the course will focus on using these concepts on diverse financial applications to gain a better practical understanding of them.
The outline of ‘Derivatives pricing and stochastic calculus 1’ course was followed in order to facilitate the synergies between both courses.
Outlines for the support course:
Comets F. and T. Meyre, Calcul Stochastique et modèle de diffusion, 324 pages. 2006.
Lamberton D. and B. Lapeyre, Introduction to Stochastic Calculus applied to finance, 256 pages. 2007.
1 final exam