Monte Carlo Methods for Financial Applications, 7.5 Credits

Contents

Monte Carlo-methods is a collection name for statistical simulation methods. The course aims to give a considerable familiarity for using Monte Carlo methods for the pricing and risk analysis of finansial derivatives. This is achieved through practical use of the methods. Special attention is given to the principles of Monte Carlo-simulation of underlying interest- and price processes, given by stochastic differential equations, different techniques for variance reduction, quasi-Monte Carlo, pricing of European and American options, and calculation of Greeks (sensitivities). 

Expected learning outcomes

For a apassing grade, the student must be able to

Knowledge and understanding

• account in detail for the principles of simulation with Monte Carlo methods

Skills and abilities

• independently simulate interest- and price processes, and apply Monte Carlo-methods för pricing financial derivatives with the simulated processes
• critically apply the methods of control variables, antithetic variables and stratified sampling in order to reduce the variance when pricing financial derivatives
• apply quasi-Monte Carlo for the pricing of financial derivatives
• use the methods in the course for calculating Greeks
• pricing american contracts, inter alia by using the regression method

Judgement and approach

• analyse and compare the results from different methods and show understanding of in what situations a certain method should be preferred

Required Knowledge

The course requires 90 ECTS including 22,5 ECTS in Calculus of which 7,5 ECTS in Multivariable Calculus and Differential Equations and a basic course in Mathematical Statistics, minimum 6 ECTS. Proficiency in English and Swedish equivalent to the level required for basic eligibility for higher studies.

Form of instruction

The teaching consists of lectures and supervised lab work.

Examination modes

The course is assessed through written lab reports and written examinations, that are assessed by one of the following judgements: Fail (U), Pass (3), Pass with merit (4) or Pass with distinction (5). For the course as a whole, one of the following grades is awarded: Fail (U), Pass (3), Pass with merit (4) or Pass with distinction (5). The grade for the whole course is determined by the grade given for Element 1.  The grade is only set once all compulsory parts have been assessed. The grade constitutes a weighted judgement of the judgements of the different parts of the examination, where the judgement of the lab reports have 70% weight, and the jufgement of the written examinations have 30% weight.

A student who has been awarded a passing grade for the course cannot be reassessed for a higher grade. Students who do not pass a test or examination on the original date are given another date to retake the examination. A student who has sat two examinations for a course or a part of a course, without passing either examination, has the right to have another examiner appointed, provided there are no specific reasons for not doing so (Chapter 6, Section 22, HEO). The request for a new examiner is made to the Head of the Department of Mathematics and Mathematical Statistics. Examinations based on this course syllabus are guaranteed to be offered for two years after the date of the student's first registration for the course.
 
Credit transfers
Students are entitled to an assessment of whether previous education or equivalent knowledge and skills acquired in professional experience can be accredited for equivalent studies at Umeå University. Applications for credit transfers must be sent to Student Services/Degree Evaluation Office. More information on credit transfers can be found on Umeå University's student website, www.student.umu.se, and in the Higher Education Ordinance (Chapter 6). Rejected applications for credit transfers can be appealed (Higher Education Ordinance, Chapter 12) to the Higher Education Appeals Board. This applies regardless of whether the rejection relates to all or parts of the credit transfer application.
 

Other regulations

In a degree, this course may not be included together with another course with a similar content. If unsure, students should ask the Director of Studies in Mathematics and Mathematical Statistics. The course can also be included in the subject area of computational science and engineering.