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:
Financial Mathematics A1F
Explanation of codes
The code indicates the education cycle and in-depth level of the course in relation to other courses within the same main field of study according to the requirements for general degrees:
- G1N: has only upper-secondary level entry requirements
- G1F: has less than 60 credits in first-cycle course/s as entry requirements
- G1E: contains specially designed degree project for Higher Education Diploma
- G2F: has at least 60 credits in first-cycle course/s as entry requirements
- G2E: has at least 60 credits in first-cycle course/s as entry requirements, contains degree project for Bachelor of Arts/Bachelor of Science
- GXX: in-depth level of the course cannot be classified
- A1N: has only first-cycle course/s as entry requirements
- A1F: has second-cycle course/s as entry requirements
- A1E: contains degree project for Master of Arts/Master of Science (60 credits)
- A2E: contains degree project for Master of Arts/Master of Science (120 credits)
- AXX: in-depth level of the course cannot be classified
- Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Established: 2012-03-08
- Established by:
- Revised: 2022-02-08
- Revised by: The Faculty Board of Science and Technology
- Applies from: Autumn 2022
120 credits including 90 credits in mathematics. Participation in Financial Derivatives. Proficiency in English equivalent to the Swedish upper secondary course English 6.
- Responsible department: Department of Mathematics
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.
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.
Lectures and computer laboratories.
Programming project during the course with an oral follow-up examination at the end of the course (10 credits).
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.
Applies from: Autumn 2022
Some titles may be available electronically through the University library.
Monte Carlo methods in financial engineering
New York: Springer, cop. 2004