# Monte Carlo Methods with Financial Applications

10 credits

Syllabus, Master's level, 1MA214

A revised version of the syllabus is available.
Code
1MA214
Education cycle
Second cycle
Main field(s) of study and in-depth level
Financial Mathematics A1F, Mathematics A1F
Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by
The Faculty Board of Science and Technology, 30 August 2018
Responsible department
Department of Mathematics

## Entry requirements

120 credits including 90 credits in mathematics. Financial Derivatives. Proficiency in English equivalent to the Swedish upper secondary course English 6.

## Learning outcomes

On completion of the course, the student should be able to:

• explain the principles for pricing financial derivatives;
• explain the principles of simulation based on Monte Carlo;
• explain Brownian motion and geometric Brownian motion in detail;
• apply methods for variance reduction in the context of pricing financial derivatives;
• explain the principles of quasi Monte Carlo and apply the method of quasi Monte Carlo in the context of pricing financial derivatives;
• apply methods of Monte Carlo to calculate sensitivity parameters for financial derivatives;
• apply methods of Monte Carlo for pricing of financial derivatives of American type.

## Content

Principles of Monte Carlo, principles of pricing financial derivatives, random number generation, general sampling methods, normal random variables and vectors, Brownian motion, geometric Brownian motion, variance reduction techniques, control variates, antithetic variates, stratified sampling, importance sampling, quasi Monte Carlo, the principles of quasi Monte Carlo, Halton sequences, Faure sequences, Sobol sequences, estimation of sensitivities, finite difference approximations, pathwise derivatives estimates, the likelihood ratio method, pricing American options, parametric approximations, random tree methods, regression based methods, the method based on duality.

## Instruction

Lectures and computer laboratories.

## Assessment

Compulsory assignments in accordance with instructions at course start.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.