401-4658-00L Computational Methods for Quantitative Finance: PDE Methods
| Semester | Spring Semester 2019 |
| Lecturers | L. Herrmann, K. Kirchner |
| Periodicity | yearly recurring course |
| Language of instruction | English |
Courses
| Number | Title | Hours | Lecturers | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 401-4658-00 V | Computational Methods for Quantitative Finance: PDE Methods Permission from lecturers required for all students.
| 3 hrs |
| L. Herrmann, K. Kirchner | ||||||
| 401-4658-00 U | Computational Methods for Quantitative Finance: PDE Methods | 1 hrs |
| L. Herrmann, K. Kirchner |
Catalogue data
| Abstract | Introduction to principal methods of option pricing. Emphasis on PDE-based methods. Prerequisite MATLAB programming and knowledge of numerical mathematics at ETH BSc level. |
| Learning 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. 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. |
| Lecture notes | There will be english, typed lecture notes as well as MATLAB software for registered participants in the course. |
| Literature | 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. N. Hilber, O. Reichmann, Ch. Schwab and Ch. Winter: Computational Methods for Quantitative Finance, Springer Finance, Springer, 2013. |
Performance assessment
| Performance assessment information (valid until the course unit is held again) | |
Performance assessment as a semester course | |
| ECTS credits | 6 credits |
| Examiners | K. Kirchner, L. Herrmann |
| Type | end-of-semester examination |
| Language of examination | English |
| Repetition | The performance assessment is only offered at the end after the course unit. Repetition only possible after re-enrolling. |
| Additional information on mode of examination | Meaningful solutions to 70% of 11 weekly 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 MATLAB programming problems. Examination will take place on ETH-workstations running MATLAB under LINUX. Own computer will NOT be required for the examination. |
| Digital exam | The exam takes place on devices provided by ETH Zurich. |
Learning materials
| Main link | Main webpage |
| Only public learning materials are listed. | |
Groups
| No information on groups available. |
Restrictions
| General | Permission from lecturers required for all students |
