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Informatique et Mathématiques appliquées
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> Formation > Cursus ingénieur

Introduction to derivative products - 4MMIPD6

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  • Number of hours

    • Lectures : 16.5
    • Tutorials : 16.5
    • Laboratory works : -
    • Projects : -
    • Internship : -
    • Written tests : -
    ECTS : 3.0
  • Officials : Jerome LELONG, Herve GUIOL

Goals

The goal of this course is to present the concepts of pricing and hedging products in continuous time. At the end of the lecture, students will know how to handle vanilla options in the one dimensional Black Scholes model. In particular they shall master the following notions :
Brownian Motion;
Continuous time martingale;
Wienner's and Itô's Integral;
Itô's formulas.

Content

  • Stochastic processes and Brownian motion
    • Gaussian vectors
    • Continuous time stochastic processes
    • Brownian motion : definition and first properties
  • Continuous time martingales
    • Filtrations and stopping times
    • Martingales : stopping time theorem, applications to Brownian motion, strong Markov property
  • Stochastic integral and Itô formula
    • Wiener's integral
    • Itô's integral
    • Itô's formula
    • Applications of Itô's formula : representing the Brownian martingales and the Cameron Martin theorem
    • Stochastic differential equations
  • The Black Scholes model
    • The underlying asset
    • Replicating strategies
    • Pricing and hedging options

Prerequisites

A first course in probability and the Stochastic processes and application to Finance lecture of the previous semester.

Tests

Continuous assessment : presence, participation, homework.

Regular Session :
A Written Exam : 2h

  1. Lexique
    CC = note de contrôle continu
    E1 = note de l'examen de session 1
    E2 = note de l'examen de rattrapage
  1. Notes transmises à la scolarité
    N1=(E1+CC)/2 # Note finale de session 1
    N2=(E2+CC)/2 # Note de session 2

Calendar

The course exists in the following branches:

  • Curriculum - Financial Engineering - Semester 8
see the course schedule for 2020-2021

Additional Information

Course ID : 4MMIPD6
Course language(s): FR

The course is attached to the following structures:

You can find this course among all other courses.

Bibliography

El Karoui N. & Gobet E. Les outils stochastiques des marchés financiers, Edition de l'Ecole Polytechnique. ISBN 978-2-7302-1579-4

Lamberton D & Lapeyre B. Introduction au calcul Stochastique appliqué à la finance, Ellipse. ISBN 2-7298-4782-0

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Date of update January 15, 2017

Université Grenoble Alpes