MM852: Computational option pricing, part 1

Entry requirements

This course cannot be taken in addition to MM542 or MM833, or if MM566 has been followed in spring 2024 or spring 2025.

Academic preconditions

Academic preconditions. Students taking the course are expected to:

a) Have knowledge of at least one of the following subjects:

Numerical solution of ordinary differential equations
Theory of stochastic integration and stochastic differential equations
Theory of option pricing

b) Be able to use Matlab or R.

The course builds on the knowledge acquired in the courses MM534 “Differential equations, Computing and Modelling”/ MM547 “Ordinary differential equations: Theory, Modelling and Simulation” or MM802 "Stochastic differential equations 1", and gives an academic basis for a Master project in several core areas of Natural Sciences.

Course introduction

The aim of the course is to enable the student to:

Model problems from financial mathematics, especially option pricing, by stochastic and partial differential equations,
Solve the resulting problem classes efficiently by computational methods based on a sound mathematical analysis,
Evaluate and select among the methodologies, tools and general skills of the subject area,
Initiate independently and carry out interdisciplinary collaboration and assume professional responsibility,
Independently take responsibility for his own professional development and specialisation.

Expected learning outcome

The learning objective of the course is that the student demonstrates the ability to:

Deal with stochastic differential equation models in finance
Analyse and simulate stochastic differential equations using appropriate, advanced methods and modern software
Design and perform reliable simulations of stochastic differential equation model

Content

The following main topics are contained in the course:

Numerical solution of stochastic differential equations
Monte Carlo simulation of stochastic differential equations, with focus on variance reduction methods, especially Multilevel Monte Carlo
Application to European, Asian, lookback, barrier and digital options

Literature

See itslearning for syllabus lists and additional literature references.

Examination regulations

Exam element a)

Timing

Spring

Tests

Project

EKA

N310049102

Assessment

Second examiner: None

Grading

Pass/Fail

Identification

Full name and SDU username

Language

Normally, the same as teaching language

Examination aids

To be announced during the course

ECTS value

Indicative number of lessons

28 hours per semester

Teaching Method

Planned lessons:

Total number of planned lessons: 28

Hereof:

Common lessons in classroom/auditorium: 28

Teaching is centred on interaction and dialogue. In the common lessons, concepts, theories and models are introduced and put into perspective. There is also place for questions and discussions and students presenting their approaches to solve some exercises, which require thorough pre- and post-processing.

Other planned teaching activities:

Immersion and preparation for the common lessons, especially reading suggested literature
Preparation of exercises in study groups

Teacher responsible

Name	E-mail	Department
Kristian Debrabant	debrabant@imada.sdu.dk	Computational Science

Additional teachers

Name	E-mail	Department	City
Simon Øster Ellegaard Andersen	siean@imada.sdu.dk	Institut for Matematik og Datalogi

Timetable

Odense

Show full time table

Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Registration

NAT

Offered in

Odense

Recommended course of study

Profile	Education	Semester	Offer period

Transition rules

Transitional arrangements describe how a course replaces another course when changes are made to the course of study.

If a transitional arrangement has been made for a course, it will be stated in the list.

See transitional arrangements for all courses at the Faculty of Science.