401-4658-00L  Computational Methods for Quantitative Finance: PDE Methods

SemesterSpring Semester 2021
LecturersC. Marcati, A. Stein
Periodicityyearly recurring course
Language of instructionEnglish


401-4658-00 VComputational Methods for Quantitative Finance: PDE Methods
Permission from lecturers required for all students.
3 hrs
Wed14:15-16:00HG D 5.2 »
Fri14:15-15:00HG D 5.2 »
C. Marcati, A. Stein
401-4658-00 UComputational Methods for Quantitative Finance: PDE Methods
Groups are selected in myStudies.
1 hrs
Fri13:15-14:00HG D 5.2 »
16:15-17:00HG D 5.2 »
C. Marcati, A. Stein

Catalogue data

AbstractIntroduction 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.
ObjectiveIntroduce 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.
Content1. 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 notesThere will be english lecture notes as well as MATLAB or Python software for registered participants in the course.
LiteratureMain 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 / NoticeKnowledge 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 credits6 credits
ExaminersC. Marcati, A. Stein
Typeend-of-semester examination
Language of examinationEnglish
RepetitionA repetition date will be offered in the first two weeks of the semester immediately consecutive.
Additional information on mode of examinationMeaningful 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 examinationThe examination may take place on the computer.

Learning materials

Main linkMain webpage
Only public learning materials are listed.


401-4658-00 UComputational Methods for Quantitative Finance: PDE Methods
Registration for groups in myStudies is possible until 15.03.2021.
Fri13:15-14:00HG D 5.2 »
Fri16:15-17:00HG D 5.2 »


GeneralPermission from lecturers required for all students
GroupsRestrictions are listed under Groups

Offered in

Data Science MasterInterdisciplinary ElectivesWInformation
Doctoral Department of MathematicsGraduate SchoolWInformation
Mathematics MasterSelection: Numerical AnalysisWInformation
Quantitative Finance MasterMathematical Methods for FinanceWInformation
Computational Science and Engineering MasterComputational FinanceWInformation
Statistics MasterStatistical and Mathematical CoursesWInformation