- Lecturer
- Christoph Schwab
- Coordinators
- Lukas Herrmann, Diyora Salimova
Exam inspection: Fri, Sept 28, 2018, 12:00 -- 13:00, HG F 33.1
First lecture: Wed, Feb 28, 2018, 2nd week of FS18, 13:15 -- 15:00 HG D1.2
Examination:
A closed-book, computer-based exam will take place
- date: June 1, 2018
- time: 13:00 until 15:00 (must arrive before 12:50)
- place: HG E 19, HG E26.3, HG E 27
- duration: 120 minutes
The exam will be similar to the homework problems. MATLAB programming will be part of the examination.
Students will take the exam on ETH workstations
with preinstalled MATLAB and
Swiss keyboard layout.
[Use of own computer is not permitted].
There will be weekly homework assignments, which are due in the break between the two hours of lecture on Wednesday, i.e. at 14:15.
Solutions to the theoretical questions can be handed in in the lecture room in paper or scanned and submitted via e-mail before the deadline.
Code must be handed in online using the submission interface.
Only in case the submission does not work: send your codes via E-Mail to your assistant and contact
Lukas Herrmann to update the configuration of the submission interface.
Submissions of problem sheets in a group are not allowed.
Each problem will be marked according to the following scheme:
- 0 - no submission
- 0.5 - incomplete or insufficient submission
- 1 - sufficient submission
- 1.5 - excellent submission.
Students who need a numerical mark
MUST take the written exam at the end of the semester.
Students who acquire at least 70% of the points attainable by
doing the weekly problem sheets, i.e., in average 0.7 points per exercise, are given an additive bonus of 0.25 on their final grade (e.g. grade 4.5 (without bonus) will be grade 4.75 (with bonus)).
Students who do not need a numerical mark
(i.e. only require a "pass" grade, which
includes D-MATH PhD students at ETH)
must achieve at least 70% of the maximal
number of points attainable by sufficient submission of the
weekly homework problem sheets, i.e. in average 0.7 points
must be achieved per problem.
Students who did not achieve the required percentage of points
in the weekly homework problem sheets can still achieve a "pass" by taking the final written exam.
| time | room | assistant | distribution by surnames |
|---|
| Fr 14-15 | HG D1.2 | Diyora Salimova (diyora.salimova@sam.math.ethz.ch) and Lukas Herrmann (lukas.herrmann@sam.math.ethz.ch) | A - K |
| Fr 14-15 | HG G5 | Lukas Gonon (lukas.gonon@math.ethz.ch) | L - Z |
For Matlab or programming related questions the teaching assistant Filip Janicki (fjanicki at student.ethz.ch) is knowledgable. Matlab file used in the Matlab tutorial on March 7 is available
here .
Lecture Material
The main methods of option pricing for efficient numerical valuation of derivative contracts in a Black-Scholes
as well as in incomplete markets due to Levy processes or due to stochastic volatility models with emphasis on PDE-based methods are introduced.
Further, implementation of pricing methods in MATLAB is developed.
- Foundations and Implementation of efficient valuation of European and exotic contracts on jump-diffusions.
- Enable participants to develop and use MATLAB implementations of these methods for the solution of pricing problems.
- Reformulation of the pricing problem as deterministic partial (integro) differential equation, for general Levy price processes and numerous types of contracts.
- Contracts covered range from algorithms for classical Black-Scholes pricing of European Vanillas to American puts to most recent,
advanced methods for pricing in incomplete markets, with prices governed by jump-diffusion processes, and to pricing in the presence of stochastic volatility.
- Modelling, analysis and implementation of the algorithms will be emphasized throughout.
Prerequisites
-
Continuous time financial modeling: Black-Scholes models, basic types of contracts:
European, American call/put (equivalent to the course "Mathematical Foundations of Finance").
- Basic stochastic calculus (Brownian Motion, Ito's Lemma ... ), some knowledge about jump-diffusion processes as e.g., in the book "Financial Modeling with Jump Diffusions".
- Basic Numerical Mathematics (A.Quarteroni, R. Sacco and F. Saleri: Numerical Mathematics, Springer, 2000).
- Basic knowledge of MATLAB.
Contents
- Review of option pricing. Wiener and Lévy price process models. Deterministic, local and stochastic volatility models.
- Finite Difference methods for option pricing.
- Finite Difference methods for Asian, American and Barrier type contracts.
- Finite Element methods for European and American style contracts.
- Pricing under local and stochastic volatility in Black-Scholes markets.
- Finite Element methods for option pricing under Lévy processes. Treatment of integro-differential operators.
- Stochastic volatility models for Lévy processes.
- Techniques for high-dimensional problems. Baskets in a Black-Scholes setting and stochastic volatility models in Black-Scholes and Lévy markets.
- Introduction to sparse grid techniques.
Matlab Links
Students of ETH can download Matlab via Stud-IDES for free (product name 'Matlab free')
The course will mainly be based on the following book:
Further Literature
- Y. Achdou, O. Pironneau: Computational Methods for Option Pricing, SIAM, 2005.
- R. Cont, P. Tankov: Financial Modelling with Jump Processes, Chapman and Hall, 2004.
- D. Lamberton, B. Lapeyre: Introduction to Stochastic Calculus Applied to Finance, Chapman and Hall, 1997, Chapters 4 and 5.
- T. von Petersdorff, C. Schwab: Wavelet Discretizations of Parabolic Integrodifferential Equations, SIAM J. Numer. Anal.
Vol.41, No.1, 2003 (reference for slides 3).
- W. Schoutens: Levy Processes in Finance, Wiley, 2003.
- R. Seydel: Tools for Computational Finance, Springer, 2002.
- P. Wilmott, J. Dewynne, S. Howison: Option Pricing: Mathematical Models and Computation, Oxford Financial Press, 1993.