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Course syllabus - Simulation

Scope

7.5 credits

Course code

MAA313

Valid from

Autumn semester 2026

Education level

First cycle

Progressive Specialisation

G2F (First cycle, has at least 60 credits in first-cycle course/s as entry requirements)

Main area(s)

Mathematics/Applied Mathematics

Organisation

Department of Business and Mathematics

Ratified

2013-02-01

Revised

2025-11-03

Literature lists

Course literature is preliminary up to 8 weeks before course start. Course literature can be valid over several semesters.

    • Ratified date: 2022-03-04
    • Latest update: 2025-05-27

    Books

    Glasserman, Paul

    Monte Carlo methods in financial engineering

    Course literature

    ISBN: 0-387-00451-3 (alk. paper)

    LIBRIS-ID: 8936733

    New York, Springer, 596 s.

Objectives

The aim of this course is to give a general introduction to several different simulation techniques, a deeper knowledge in Monte Carlo simulation, explain the advantage as well as the disadvantage of the use of different simulation techniques and to give examples of applications in finance.

Learning outcomes

At the end of the course the student is expected to be able to

  • use bootstrapping, Monte-Carlo simulation and historical simulation, and be able to determine risk measures such as VaR using these techniques.
  • determine the number of simulations needed to minimize the error between Monte-Carlo approximation and real price.
  • generate random variables for continuous & discrete distributions.
  • generate trajectories of stochastic processes. (GBM, Poisson).
  • determine the fair price of American, Barrier, Asian, lookback type of financial contracts using Monte-Carlo simulation.
  • use Variance reduction techniques in Monte-Carlo simulation when determine the fair price of financial contracts.

Course content

Bootstrapping, historical simulation, Monte-Carlo simulation. Generation of random variables from distributions: normal, exponential, gamma, lognormal, student´s, Poisson Rayleigh, uniform. Generation of stochastic processes, geometrical Brownian motion, Poisson process, multivariate geometrical Brownian motion. Cholesky SVD decomposition. Variance reduction techniques. Financial contracts: American option contract barrier option contracts, Asian option, lookback option. Risk measures: Value at risk.

Specific requirements

At least totally 60 credits in the technical, natural sciences, business administration or economics areas including Methods of Statistical Inference, 7.5 credits, of which 3 credits must be completed at the beginning of the course, or the equivalent.

Examination

Computer exercises (PRO1), 4.5 credits, marks Pass (G) or Pass with distinction (VG)
Written examination (TEN1), 3 credits, marks Pass (G) or Pass with distinction (VG)

A student who has a certificate from MDU regarding disability study support, can request adaptions for the examination. It is the examiner who takes decisions on any adaptions, based on the certificate and other conditions.

Grade

Three-grade scale