401-4658-00L Computational Methods for Quantitative Finance: PDE Methods
| Semester | Spring Semester 2021 |
| Lecturers | C. Marcati, A. Stein |
| 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 |
| C. Marcati, A. Stein | ||||||
| 401-4658-00 U | Computational Methods for Quantitative Finance: PDE Methods Groups are selected in myStudies. | 1 hrs |
| C. Marcati, A. Stein |
Catalogue data
| Abstract | Introduction to principal methods of option pricing. Emphasis on PDE-based methods. Prerequisite MATLAB and Python programming and 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. |
| 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. |
| Prerequisites / Notice | Knowledge of Numerical Analysis/ Scientific Computing Techniques corresponding roughly to BSc MATH or BSc RW/CSE at ETH is expected. Basic programming skills in MATLAB or Python are required for the exercises, and are _not_ taught in this course. |
Performance assessment
| Performance assessment information (valid until the course unit is held again) | |
Performance assessment as a semester course | |
| ECTS credits | 6 credits |
| Examiners | C. Marcati, A. Stein |
| Type | end-of-semester examination |
| Language of examination | English |
| Repetition | A repetition date will be offered in the first two weeks of the semester immediately consecutive. |
| 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. |
| Online examination | The examination may take place on the computer. |
Learning materials
| Main link | Main webpage |
| Only public learning materials are listed. | |
Groups
| 401-4658-00 U | Computational Methods for Quantitative Finance: PDE Methods | ||||||
| Registration for groups in myStudies is possible until 15.03.2021. | |||||||
| Groups | G-01 |
| |||||
| G-02 |
| ||||||
Restrictions
| General | Permission from lecturers required for all students |
| Groups | Restrictions are listed under Groups |
