- 4MMICSF

Goal(s)

This course aims to introduce the mathematical concepts used for valuing and hedging derivatives in continuous time.

Upon completion of this course, students should have mastered the following concepts: Brownian motion; continuous-time martingales; Wiener and Itô integrals; Itô's formula; and will have had an initial presentation on pricing and hedging a call option in the Black-Scholes model on a single asset.

Responsible(s)

Christophe DUTANG, Hervé GUIOL

Content(s)

The course is structured in 4 parts:

• Brownian Motion and Processes
  • Gaussian Vectors
  • Continuous-Time Processes
  • Brownian Motion: Definition and Initial Properties
  • Continuous-Time Martingales
  • Filtrations and Stopping Times
  • Martingales: Stopping Theorem
  • Application to Brownian Motion, Strong Markov Property
  • Stochastic Integral and Itô's Formula
  • Wiener Integral
  • Itô's Integral
  • Itô's Formula
  • Applications of Itô's Formula
  • Representation of Brownian Martingales
  • Cameron Martin Theorem
  • Stochastic Differential Equations
• Black-Scholes Model
  • The Evolution Model
  • The Concept of Strategy
  • Option Valuation and Hedging

Course 2A: Advanced Probability and Statistics 1

Test

Evaluation : 40% of Participation et assiduité and 60% of Examen écrit (3h)

Resit : Examen écrit (2h)

In the first session, the continuous assessment grade is based on attendance, participation, and the various assignments submitted on Teide throughout the course.

The final exam is a written, in-class exam.

Permitted materials: one handwritten A4 sheet of paper
Prohibited materials: any other documents

In the second session, a written exam (2 hours) is scheduled.

Calendar

The course exists in the following branches:

• Curriculum - Core curriculum - Semester 8

Additional Information

Course ID : 4MMICSF
Course language(s):

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