Ensimag Rubrique Formation 2022

Valo - 5MMVCPD

  • Number of hours

    • Lectures 18.0
    • Projects -
    • Tutorials -
    • Internship -
    • Laboratory works -
    • Written tests -


    ECTS 2.0


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 3h session 1, 2h session 2,
No document allowed but a 1 page handscript summary

    • MCC en présentiel **
      N1=(CC +2E1)/3
    • MCC en distanciel **
      N1=(CC +2Devoir1)/3


The course exists in the following branches:

  • Curriculum - Financial Engineering - Semester 9
see the course schedule for 2023-2024

Additional Information

Course ID : 5MMVCPD
Course language(s): FR

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