Computational Methods for Quantitative Finance: PDE Methods
Please note that this page is old.
Check in the VVZ
for a current information.
May 28th, 13.00-15.00
ETH HG E 19 and ETH HG E 27
Question Time : Wed. 15-16 in HG G 53
There will be homework assignments.
To get the ECTS credit points, all students (except PhD students) must participate in the end-of-semester exam and must pass it.
Solved exercises can be turned in into the box
located at the entry to room HG G53.
We strongly advise all students to complete the homework assignments, the understanding of the assignments is crucial to passing the end-of-semester exam.
Aims of the course
The main methods of option pricing for efficient numerical valuation of derivative contracts in a Black-Scholes as well as in incomplete markets due to Levy processes or due to stochastic volatility models with emphasis on PDE-based methods are introduced. Further, implementation of pricing methods in MATLAB is developed.
- Foundations and Implementation of efficient valuation of European and exotic contracts on jump-diffusions.
- Enable participants to develop and use MATLAB implementations of these methods for the solution of pricing problems.
- Reformulation of the pricing problem as deterministic partial (integro) differential equation, for general Levy price processes and numerous types of contracts.
- Contracts covered range from algorithms for classical Black-Scholes pricing of European Vanillas to American puts to most recent, advanced methods for pricing in incomplete markets, with prices governed by jump-diffusion processes, and to pricing in the presence of stochastic volatility.
- Modelling, analysis and implementation of the algorithms will be emphasized throughout.
- Continuous time financial modeling: Black-Scholes models, basic types of contracts: European, American call/put.
- Basic stochastic calculus (Brownian Motion, Ito's Lemma ... ), some knowledge about jump-diffusion processes as e.g., in the book Financial Modeling with Jump Diffusions
- Basic Numerical Mathematics (A.Quarteroni, R. Sacco and F. Saleri: Numerical Mathematics, Springer, 2000)
- Basic knowledge of MATLAB.
- Review of option pricing. Wiener and Lévy price process models. Deterministic, local and stochastic volatility models.
- Finite Difference methods for option pricing.
- Finite Difference methods for Asian, American and Barrier type contracts.
- Finite Element methods for European and American style contracts.
- Pricing under local and stochastic volatility in Black-Scholes markets.
- Finite Element methods for option pricing under Lévy processes. Treatment of integro-differential operators.
- Stochastic volatility models for Lévy processes.
- Techniques for high-dimensional problems. Baskets in a Black-Scholes setting and stochastic volatility models in Black-Scholes and Lévy markets.
- Introduction to sparse grid techniques.
Students of ETH can download Matlab via Stud-IDES for free (product name 'Matlab free')
Prime Literature Reference
The course will mainly be based on the following book:
- N. Hilber, O. Reichmann, Ch. Schwab, Ch. Winter: Computational Methods for Quantitative Finance, Springer Finance, Springer, 2013.
There will be a link on the exercise webpage granting you access to the lecture material.
- Y. Achdou, O. Pironneau: Computational Methods for Option Pricing, SIAM, 2005.
- R. Cont, P. Tankov: Financial Modelling with Jump Processes, Chapman and Hall, 2004.
- D. Lamberton, B. Lapeyre: Introduction to Stochastic Calculus Applied to Finance, Chapman and Hall, 1997, Chapters 4 and 5.
- M. Guenther, A. Juengel: Finanzderivate mit MATLAB, Vieweg, 2003
- W. Schoutens: Levy Processes in Finance, Wiley, 2003.
- R. Seydel: Tools for Computational Finance, Springer, 2002.
- P. Wilmott, J. Dewynne, S. Howison: Option Pricing: Mathematical Models and Computation, Oxford Financial Press, 1993.