Coursebooks 2017-2018

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Computational finance

FIN-472

Lecturer(s) :

Mokak Teguia Alberto
Pulido Nino Sergio Andres

Language:

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

Required courses

Stochastic processes / stochastic calculus

Recommended courses

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:

Transversal skills

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

Virtual desktop infrastructure (VDI)

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

In the programs

  • Financial engineering, 2017-2018, Master semester 1
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Computational finance
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Financial engineering, 2017-2018, Master semester 3
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Computational finance
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Applied Mathematics, 2017-2018, Master semester 1
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Computational finance
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Applied Mathematics, 2017-2018, Master semester 3
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Computational finance
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Mathematics - master program, 2017-2018, Master semester 1
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Computational finance
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Mathematics - master program, 2017-2018, Master semester 3
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Computational finance
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Mathematics for teaching, 2017-2018, Master semester 1
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Computational finance
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Mathematics for teaching, 2017-2018, Master semester 3
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Computational finance
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Computational science and Engineering, 2017-2018, Master semester 1
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Computational finance
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Computational science and Engineering, 2017-2018, Master semester 3
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Computational finance
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks

Reference week

MoTuWeThFr
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
Lecture
Exercise, TP
Project, other

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  • Winter sessions
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  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German