401-4658-00L Computational Methods for Quantitative Finance: PDE Methods
| Semester | Frühjahrssemester 2018 |
| Dozierende | C. Schwab |
| Periodizität | jährlich wiederkehrende Veranstaltung |
| Lehrsprache | Englisch |
Lehrveranstaltungen
| Nummer | Titel | Umfang | Dozierende | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 401-4658-00 V | Computational Methods for Quantitative Finance: PDE Methods Bewilligung der Dozierenden für alle Studierenden notwendig.
| 3 Std. |
| C. Schwab | ||||||
| 401-4658-00 U | Computational Methods for Quantitative Finance: PDE Methods | 1 Std. |
| C. Schwab |
Katalogdaten
| Kurzbeschreibung | Introduction to principal methods of option pricing. Emphasis on PDE-based methods. Prerequisite MATLAB programming and knowledge of numerical mathematics at ETH BSc level. |
| Lernziel | 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. |
| Inhalt | 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. |
| Skript | There will be english, typed lecture notes as well as MATLAB software for registered participants in the course. |
| Literatur | 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. |
| Voraussetzungen / Besonderes | Start of the lecture: WED, 28 Feb. 2018 (second week of the semester). |
Leistungskontrolle
| Information zur Leistungskontrolle (gültig bis die Lerneinheit neu gelesen wird) | |
Leistungskontrolle als Semesterkurs | |
| ECTS Kreditpunkte | 6 KP |
| Prüfende | C. Schwab |
| Form | Semesterendprüfung |
| Prüfungssprache | Englisch |
| Repetition | Die Leistungskontrolle wird nur am Semesterende nach der Lerneinheit angeboten. Die Repetition ist nur nach erneuter Belegung möglich. |
| Zusatzinformation zum Prüfungsmodus | 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. |
| Digitale Prüfung | Die Prüfung findet auf Geräten statt, die von der ETH Zürich zur Verfügung gestellt werden. |
Lernmaterialien
| Hauptlink | Main webpage |
| Es werden nur die öffentlichen Lernmaterialien aufgeführt. | |
Gruppen
| Keine Informationen zu Gruppen vorhanden. |
Einschränkungen
| Allgemein | Bewilligung der Dozierenden für alle Studierenden notwendig |
