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We first deal with the fundamental tools of Stochastic Calculus. Then we deal with the valuation and hedging of financial products in a multi-asset context.
Itô integral- Itô lemma - Girsanov theorem- change of numeraire - valuation theorem - risk neutral pricing and hedging- Examples
"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
I. Karatzas, S.E. Shreve "Brownian motion and stochastic calculus", SpringerS.E. Shreve "Stochastic Calculus for Finance, Volume II: Continuous-Time Models".