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|
|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|
2. Finite Difference Methods for option pricing. Relation to bi- and multinomial trees.
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
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.
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.