Course syllabus - Simulation

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.

Tuition

Lectures where theory, methods and problems are discussed.

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 a disability has the opportunity to submit a request for supportive measures during written examinations or other forms of examination, in accordance with the Rules and Regulations for Examinations at First-cycle and Second-cycle Level at Mälardalen University (2020/1655). It is the examiner who takes decisions on any supportive measures, based on what kind of certificate is issued, and in that case which measures are to be applied.

Suspicions of attempting to deceive in examinations (cheating) are reported to the Vice-Chancellor, in accordance with the Higher Education Ordinance, and are examined by the University’s Disciplinary Board. If the Disciplinary Board considers the student to be guilty of a disciplinary offence, the Board will take a decision on disciplinary action, which will be a warning or suspension.

Grade

Three-grade scale