# Syllabus for Monte Carlo Methods with Financial Applications

Monte Carlo-metoder med finansiella tillämpningar

• 10 credits
• Course code: 1MA214
• Education cycle: Second cycle
• Main field(s) of study and in-depth level: Mathematics A1F, Financial Mathematics A1F
• Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
• Established: 2012-03-08
• Established by:
• Revised: 2018-08-30
• Revised by: The Faculty Board of Science and Technology
• Applies from: week 24, 2019
• Entry requirements: 120 credits including 90 credits in mathematics. Financial Derivatives.
English language proficiency that corresponds to English studies at upper secondary (high school) level in Sweden ("English 6").
• Responsible department: Department of Mathematics

## 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.