25874 Numerical Methods in Finance
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Credit points: 8 cp
Subject level:
Postgraduate
Result type: Grade and marksThere are course requisites for this subject. See access conditions.
Description
The subject covers the theoretical and practical aspects of numerical methods for pricing and hedging options. There is a strong emphasis on programming, with students learning how to implement the various techniques themselves.
Subject learning objectives (SLOs)
Upon successful completion of this subject students should be able to:
| 1. | define and illustrate the terms used in Numerical Analysis in Finance |
|---|---|
| 2. | demonstrate and apply discrete time approximation techniques for stochastic differential equations |
| 3. | simulate the solution of problems involving stochastic differential equations, jump diffusions and solve numerically partial differential equations |
| 4. | describe modern statistical and filtering methods with applications in finance |
| 5. | clearly communicate knowledge of the subject matter in numerical and financial contexts and the solutions to problems requiring such knowledge. |
Contribution to the development of graduate attributes
This subject provides an overview of the theoretical and practical aspects of the numerical methods used in quantitative finance. It contributes to the objectives of the course by giving students practically useful tools to compute reliable and robust option prices and hedge ratios.
This subject contributes to the development of the following graduate attributes:
- Critical thinking, creativity and analytical skills
- Business practice oriented skills
This subject also contributes specifically to develop the following Program Learning Objectives for the Master of Quantitative Finance:
- 2.1: Apply innovative new financial models to address financial trading and risk management issues
- 5.1: Master quantitative finance technical skills necessary for professional practice
Teaching and learning strategies
The subject is presented in seminar format. Numerical techniques are presented and analysed during the lecture, after which the students are guided through worked examples that illustrate various implementation issues. They are then required to implement the techniques themselves in an assigned programming language, in order to solve prescribed homework problems. Programming is a significant component of the subject.
Content (topics)
- Random number generation
- Generating stock price paths
- Monte Carlo methods
- Variance reduction techniques
- Quasi-Monte Carlo methods
- Explicit finite difference schemes
- Implicit difference schemes
- Binomial and trinomial lattices
- Calibrating the volatility surface
Assessment
Assessment task 1: Assignments (Individual)
| Weight: | 50% |
|---|
Assessment task 2: Final Exam (Individual)
| Weight: | 50% |
|---|
Minimum requirements
Students must achieve at least 50% of the subject’s total marks.
References
Platen, E. and Bruti-Liberati, N. (2010) Numerical Solution of Stochastic Differential Equations with Jumps in Finance, Springer.
Kloeden, P.E. and Platen, E. (1999) Numerical Solution of Stochastic Differential Equations, Vol 23 of Applied Math., Springer, Third corrected printing. Kloeden, P.E; Platen, E. and Schurz, H. (2003} Numerical Solution of SDE's Through Computer Experiments, Universitext, Springer, Third corrected printing.
Platen, E. and Heath, D. (2010) A Benchmark Approach to Quantitative Finance, Springer Finance. Seydel, R. (2002) Tools for Computative Finance, Universitext, Springer. Wilmott, P.; Dewynne, J. and Howison, S. (1996) Option Pricing: Mathematical Models and Computation, Oxford Financial Press
Press, W. H., Teukolsky, Saul A., Vetterling, William T., and Flannery, Brian P., Numerical Recipes: The Art of Scientific Computing, 3rd edition, Cambridge University Press, 2007
Smith, G. D., Numerical Solution of Partial Differential Equations: Finite Difference Methods, 2nd edition, Cambridge University Press, 1978
Wilmott, P., Dewynne, J., and Howison, S., Option Pricing: Mathematical Models and Computation, Oxford Financial Press, 1993
Other resources
1. Reading Material
The course will be based on the book "Numerical Solution of SDEs with Jumps in Finance" by Eckhard Platen and Nicola Bruti-Liberati and the book "A Benchmark Approach to Quantitative Finance" by Eckhard Platen and David Heath.
2. Lecture Slides
The presented lecture slides will be provided electronically as course material.
3. Exercises
Exercises are included in the lecture notes at the end of each chapter.
4. Program Templates
Lab Tasks and Projects will be provided separately. Computerlab activities and schedule will be provided separately.