Fiches de cours 2017-2018

Computational finance

Enseignant(s) :

Mokak Teguia Alberto
Pulido Nino Sergio Andres

English

Summary

Participants of this course will master computational techniques frequently used in mathematical finance applications. Emphasis will be put on the implementation and practical aspects.

Content

1. Brief introduction to option pricing
Basic stochastic models in finance
Basic tools of stochastic calculus
Monte Carlo simulation based methods

2. Transformation based methods
Affine models
Option pricing via Fourier transforms

3. Density approximation techniques
Polynomial models and calculation of moments
Option pricing via density approximation

4. Option pricing via PDE models
Finite difference approximation of Black-Scholes PDE
American options and free boundary problems
Jump-diffusion processes and integro-differential equations

Keywords

financial models, stochastic calculus, option pricing, numerical methods, Matlab, Monte Carlo simulation, PDE, Fourier transform, density approximation techniques, volatility surface

Learning Prerequisites

Recommended courses

Stochastic processes / stochastic calculus

Numerical Analysis

Introduction to Finite Elements

Derivatives

Important concepts to start the course

Basic background in numerical analysis, linear algebra, and differential equations.
Command of Matlab.

Learning Outcomes

By the end of the course, the student must be able to:
• Choose method for solving a specific pricing or calibration problem.
• Implement numerical algorithms.
• Interpret the results of a computation.
• Recall the advantages and limitations of different methods.
• Assess / Evaluate the performance of several financial models.
• Compare the results from different pricing algorithms.
• Recall the basic concepts behind the theory of option pricing in financial models.

Transversal skills

• Use a work methodology appropriate to the task.

Teaching methods

Ex cathedra lecture, exercises in the classroom and with computer.

Expected student activities

Attendance of lectures.
Completing exercises.
Solving problems on the computer.

Assessment methods

Computer-based final examination. 20% of the grade are determined by take-home exams / graded exercises.

Resources

No

Bibliography

Hirsa, Ali. Computational methods in finance. Chapman & Hall/CRC Financial Mathematics Series. CRC Press, Boca Raton, FL, 2013.

Seydel, Rüdiger U. Tools for computational finance. Fourth edition. Universitext. Springer-Verlag, Berlin, 2009.

Achdou, Yves; Pironneau, Olivier Computational methods for option pricing. Frontiers in Applied
Mathematics, 30. SIAM, Philadelphia, PA, 2005.

Björk, Tomas. Arbitrage Theory in Continuous Time. Third edition, OUP Oxford, 2009.

Shreve, Steven E. Stochastic Calculus for Finance II: Continuous-Time Models, Volume 11. Springer Science & Business Media, 2004.

Lamberton, Damien; Lapeyre, Bernard. Introduction to stochastic calculus applied to finance. Second revised edition. Chapman & Hall/CRC, 2008.

Additional lecture material will be provided by the instructors.

Notes/Handbook

' Computational methods in finance / Hirsa
' Tools for computational finance / Seydel
' Computational methods for option pricing / Achdou
' Arbitrage Theory in Continuous Time /  Björk
' Stochastic Calculus for Finance II: Continuous-Time Models / Shreve
' Introduction to stochastic calculus applied to finance / Lamberton

Semaine de référence

LuMaMeJeVe
8-9    CHB331
9-10
10-11    CHB331
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22

Cours
Exercice, TP
Projet, autre

légende

• Semestre d'automne
• Session d'hiver
• Semestre de printemps
• Session d'été
• Cours en français
• Cours en anglais
• Cours en allemand