Ensimag Rubrique Formation 2022

Valuation and hedging of derivatives - 5MMVCPD

  • Number of hours

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

    ECTS

    ECTS 2.0

Goal(s)

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.

Responsible(s)

Herve GUIOL

Content(s)

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.

Prerequisites

"Introduction to stochastic calculus and applications to finance" ENSIMAG 2A.

In any case, some knowledge of random processes and Brownian motion are required.

Test

Evaluation : 33% of Participation et assiduité and 67% of Examen Ecrit (2h)

Resit : 33% of Participation et assiduité (reported score) and 67% of Examen Ecrit (2h)

Continuous assesment : participation and resolution of exercises in classroom.
Final exam for session 1 and session 2 : written 2h session 1, 2h session 2,
No document allowed but a 1 page handscript summary

Calendar

The course exists in the following branches:

see the course schedule for 2025-2026

Additional Information

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

The course is attached to the following structures:

  • Team Finance.
  • Team Probability-Statistics

You can find this course among all other courses.

Bibliography

S.E. Shreve "Stochastic Calculus for Finance, Volume II: Continuous-Time Models".
I. Karatzas, S.E. Shreve "Brownian motion and stochastic calculus", Springer