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MM542: Computational Option Pricing (10 ECTS)

STADS: 13012201

Level
Bachelor course

Teaching period
The course is offered in the spring semester.

Teacher responsible

Email: debrabant@imada.sdu.dk

Timetable

Group	Type	Day	Time	Classroom	Weeks
Common	I	Tuesday	10-12	U11	6
Common	I	Tuesday	10-12	U155	8-10,12-14,16-21
Common	I	Tuesday	10-12	U10	11
H1	TE	Thursday	12-14	U11	18
H1	TE	Thursday	12-14	U10	19
H1	TE	Friday	12-14	U143	6
H1	TE	Friday	12-14	U142	8,13
H1	TE	Friday	12-14	U153	9-10
H1	TE	Friday	12-14	U48A	11
H1	TE	Friday	12-14	U11	12,14,17,20-21
H1	TE	Friday	12-14	U23A	16

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Comment:
Ubegrænset deltagerantal. Undervises fælles med MM833

Prerequisites:
None

Academic preconditions:

Students taking the course are expected to:

Have knowledge of at least two of the following subjects:
Numerical solution of ordinary differential equations
Numerical solution of partial differential equations
Theory of stochastic integration and stochastic differential equations
Theory of option pricing
Be able to use Matlab, Fenics or R

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 theoretical and practical issues as well as explain the reasons for and choose relevant solution models,
Participate independently in interdisciplinary collaboration with a professional approach,
Identify his own learning needs and organise his own learning.

The course builds on the knowledge acquired in the courses MM534 “Differential equations, Computing and Modelling”/ MM547 “Ordinary differential equations: Theory, Modelling and Simulation” and MM530 “Partial Differential Equations and Numerics”/ MM546 “Partial differential equations: Theory, Modelling and Simulation”, and gives an academic basis for a Bachelor project in several core areas of Natural Sciences.

In relation to the competence profile of the degree it is the explicit focus of the course to:

Give the competence to handle complex and development-oriented situations in study and work contexts.
Give skills to:

a)analyse practical and theoretical problems with the help of numerical simulation based on a suitable mathematical model

b)describe and evaluate sources of error for the modelling and calculation of a given problem

c)justify relevant models for analysis and solution and choose between them

Give knowledge and understanding of:

a)Mathematical modelling and numerical analysis in finance

b)reflection on theories, methods and practices in the field of applied mathematics

Expected learning outcome

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

Deal with stochastic and partial differential equation models in finance
Analyse and simulate stochastic and partial differential equations by the methods taught in the course.
Construct, implement and analyse numerical methods to compute approximate solutions of stochastic and partial differential equations
Give an oral presentation and answer supplementary questions on the course syllabus and the problems solved in mandatory assignments

Subject overview

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
Numerical simulation of weak solutions of linear parabolic differential equations by the finite element method
Application to European, Asian, lookback, barrier and digital options, European options with local volatility, Lévy driven assets and stochastic volatility
Numerical simulation of American options

Literature

Meddeles ved kursets start.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam

Mandatory assignments. Pass/fail, internal evaluation by teacher. (13012212)

Assessment and marking:

Oral exam (10 ECTS). Danish 7-mark scale, internal evaluation. (13012202)

Expected working hours
The teaching method is based on three phase model.
Intro phase: 28 hours
Skills training phase: 28 hours, hereof:
- Tutorials: 28 hours

Educational activities

Reading suggested literature
Preparation of exercises in study groups
Preparation of projects
Contributing to online learning activities related to the course

Educational form

Teaching is centred on interaction and dialogue. In the intro phase, concepts, theories and models are introduced and put into perspective. In the training phase, students train their skills through exercises and dig deeper into the subject matter. In the study phase, students gain academic, personal and social experiences that consolidate and further develop their scientific proficiency. Focus is on immersion, understanding, and development of collaborative skills.

Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Remarks

The course is co-read with: MM833 “Computational Option Pricing”

The course cannot be chosen by students who: followed MM833

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.