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401-4658-00L 6 Credits MSC D-ITET , D-INFK , D-MATH
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Numerical Methods for Finance

Lecturers & Examiners: Prof. Dr. Christoph Schwab, Dr. Andreas Stein
VVZ CR n/a

Last Updated: 2026-02-05 16:22:58

Abstract

Introduction to principal methods of option pricing. Emphasis on PDE-based methods. Prerequisite MATLAB and Python programmingand knowledge of numerical mathematics at ETH BSc level.

Objective

Introduce the main methods for efficient numerical valuation of derivative contracts in a Black Scholes as well as in incomplete markets due Levy processes or due to stochastic volatility models. Develop implementation of pricing methods in MATLAB and Python. Finite-Difference/ Finite Element based methods for the solution of the pricing integrodifferential equation.

Content

1. Review of option pricing. Wiener and Levy price process models. Deterministic, local and stochastic volatility models. 2. Finite Difference Methods for option pricing. Relation to bi- and multinomial trees. European contracts. 3. Finite Difference methods for Asian, American and Barrier type contracts. 4. Finite element methods for European and American style contracts. 5. Pricing under local and stochastic volatility in Black-Scholes Markets. 6. Finite Element Methods for option pricing under Levy processes. Treatment of integrodifferential operators. 7. Stochastic volatility models for Levy processes. 8. Techniques for multidimensional problems. Baskets in a Black-Scholes setting and stochastic volatility models in Black Scholes and Levy markets. 9. Introduction to sparse grid option pricing techniques.

Resources

Lecture Notes

There will be english lecture notes as well as MATLAB or Python software for registered participants in the course.

Literature

Main reference (course text): N. Hilber, O. Reichmann, Ch. Schwab and Ch. Winter: Computational Methods for Quantitative Finance, Springer Finance, Springer, 2013. Supplementary texts: R. Cont and P. Tankov : Financial Modelling with Jump Processes, Chapman and Hall Publ. 2004. Y. Achdou and O. Pironneau : Computational Methods for Option Pricing, SIAM Frontiers in Applied Mathematics, SIAM Publishers, Philadelphia 2005. D. Lamberton and B. Lapeyre : Introduction to stochastic calculus Applied to Finance (second edition), Chapman & Hall/CRC Financial Mathematics Series, Taylor & Francis Publ. Boca Raton, London, New York 2008. J.-P. Fouque, G. Papanicolaou and K.-R. Sircar : Derivatives in financial markets with stochastic volatility, Cambridge Univeristy Press, Cambridge, 2000.

General Information

Language
English
Levels
MSC
Frequency
Yearly recurring

Examination

Type
end-of-semester examination
Mode
written 120 minutes
Aids
None
Digital
The exam takes place on devices provided by ETH Zurich.
Meaningful solutions to 70% of the homework assignments can count as bonus of up to +0.25 of final grade.End-of-Semester examination will be *closed book*, 2hr in class, and will involve theoretical as well as Python/MATLAB programming problems.Examination will take place on ETH-workstations running Python/MATLAB under LINUX. Own computer will NOT be required for the examination.

Course Components

Type Title Time & Place Hours
lecture Numerical Methods for Finance (formerly Computational Methods for Quantitative Finance: PDE Methods)
Permission from lecturers required for all students.
  • Wed 14:15-16:00 (HG D 5.2)
  • Fri 14:15-15:00 (HG D 5.2)
3 h weekly
exercise Numerical Methods for Finance (formerly Computational Methods for Quantitative Finance: PDE Methods)
Groups are selected in myStudies.
  • Fri 13:15-14:00 (HG D 5.2)
  • Fri 15:15-16:00 (HG D 5.2)
1 h weekly

Offered In