The main objective of this course is to apply the stochastic calculation on the valuation and hedging problems of financial products in a general multi underlying framework. The classic models (Black-Scholes-Merton) will be reviewed from this angle as well as on the one hand rate models and on the other hand models with local volatility. Significant emphasis will be placed on the risk neutral approach.
The course outline will follow the scheme:
Integrals and Itô formulas multidimensional case;
Black-Scholes-Merton equation, for EDP view;
Multivariate Stochastic Computation, trajectory approach;
Neutral risk valuation: Girsanov theorem, probability neutral probability, representation of Brownian Martingales, Fundamental pricing theorems;
Back to the EDP approach: Feynman-Kac 1d and muti-d formula;
Models with local volatility: Dupire formula.
"Introduction to stochastic calculus and applications to finance" ENSIMAG 2A.
In any case, some knowledge of random processes and Brownian motion are required.
Give kind of exam for session 1 and session 2: written, allowed documents or not, oral, practical work, reports, plan, vivas
The course exists in the following branches:
Course ID : 5MMGDRF
The course is attached to the following structures:
You can find this course among all other courses.
S.E. Shreve "Stochastic Calculus for Finance, Volume II: Continuous-Time Models".
I. Karatzas, S.E. Shreve "Brownian motion and stochastic calculus", Springer
Date of update July 6, 2015