MM833: Computational Option Pricing (10 ECTS)

STADS: 13012301

Level
Master's level course approved as PhD course

Teaching period
The course is offered in the spring semester.

Teacher responsible
Email: debrabant@imada.sdu.dk

Timetable
Show entire timetable
Show personal time table for this course.

Comment:
Ubegrænset deltagerantal. Undervises fælles med MM542

Prerequisites:
None

Academic preconditions:
Students taking the course are expected to:

• Have knowledge of at least two of the following subjects:
1. Numerical solution of ordinary differential equations
2. Numerical solution of partial differential equations
3. Theory of stochastic integration and stochastic differential equations
4. 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 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.

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 MM830 “Partial Differential Equations and Numerics”/ MM834 “Partial differential equations: Theory, Modelling and Simulation”, and gives an academic basis for a Master 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:
1. analyse practical and theoretical problems with the help of numerical simulation based on a suitable mathematical model
2. describe and evaluate sources of error for the modelling and calculation of a given problem
3. justify relevant models for analysis and solution and choose between them
• Give knowledge and understanding of:
1. Mathematical modelling and numerical analysis in finance
2. reflection on theories, methods and practices in the field of applied mathematics

Expected learning outcome


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

1. Mandatory assignments must be passed to participate in the exam. The assignments are evaluated on a pass/fail basis. (13012312).

Assessment and marking:

1. Oral exam, is evaluated by internal censorship by the Danish 7-mark scale (10 ECTS). (13012302).

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 Study phase: 56 hours

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.Educational form

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

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
This course is taught together with MM542 “Computational Option Pricing”. The course MM833 cannot be taken in addition to MM542.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.