Syllabus for Monte Carlo Methods with Financial Applications

Monte Carlo-metoder med finansiella tillämpningar

A revised version of the syllabus is available.

Syllabus

  • 10 credits
  • Course code: 1MA214
  • Education cycle: Second cycle
  • Main field(s) of study and in-depth level: Mathematics A1F, 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:

    First cycle

    • 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

    Second cycle

    • 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: The Faculty Board of Science and Technology
  • Applies from: Autumn 2012
  • Entry requirements: 120 credits including 90 credits in mathematics. Financial Derivatives.
  • Responsible department: Department of Mathematics

Learning outcomes

In order to pass 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.

Reading list

Reading list

Applies from: Autumn 2012

Some titles may be available electronically through the University library.

  • Glasserman, Paul Monte Carlo methods in financial engineering

    New York: Springer, cop. 2004

    Find in the library

    Mandatory