Registry

Module Specifications

Current Academic Year 2012 - 2013
Please note that this information is subject to change.

Module Title	Monte Carlo Methods in Finance
Module Code	MS551
School	School of Mathematics
Online Module Resources
Module Co-ordinator	Semester 1: Olaf Menkens Semester 2: Olaf Menkens Autumn: Olaf Menkens
Module Teacher	Olaf Menkens
NFQ level	8	Credit Rating	7.5
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

Description

The aim of this course is to provide students with a thorough and deep understanding of the Monte Carlo method, which is very important in finance as well as other areas. More specifically, the course discusses the generation of random numbers, random variables, and sample paths of random processes. Additionally, this know-how and skills module covers various variance reduction techniques and quasi-Monte Carlo methods.Students will participate in the following learning activities:Lectures: Students will attend a series of lectures designed to introduce learners to the mathematical principles and techniques that underpin this module.Tutorials: Each student (or each group of students) is given a specific assignment which usually includes to program the crude Monte Carlo method as well as an advanced Monte Carlo method, to compare the outcome, and to write a report on this.Reading: Students are expected to fully utilise the textbooks and other resources listed below.

Learning Outcomes

1. Construct, test, and implement various random number generators such as LCG, lagged Fibonacci generators, and F_2-linear generator, as well as construct and implement sample paths from uniformly distributed random numbers.
2. Calculate and programme the crude Monte Carlo method as well as advanced Monte Carlo methods such as variance reduction methods and quasi-Monte Carlo methods.
3. Identify and implement an appropriate Monte Carlo method for a specific problem and optimise the simulation (minimise speed/error) using an advanced Monte Carlo Method.
4. Validate uniformly distributed random number generators using various tests.
5. Prepare a written report detailing the implementation of a Monte Carlo method to a specific problem in Finance (such as pricing exotic options, use advanced pricing models (e.g. stochastic volatility, CEV, or variance gamma), or calculating VaR).

Workload	Full-time hours per semester
*Type*	*Hours*	*Description*
Lecture	36	No Description
Laboratory	12	Computer Lab
Independent learning time	140	No Description
Total Workload: 188

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Short reminder: The basic Monte Carlo method.
Strong law of large numbers, central limit theorem, error estimation for Monte Carlo method..

Generating pseudo-random numbers and random variables.
(Reminder:) Linear congruential generator, Mersenne Twister, Spectral test, (Reminder:) inverse transformation method and acceptance-rejection method, generating univariate and multivariate normal samples..

Generating sample paths.
Brownian motion, geometric Brownian motion, square-root diffusion..

Variance Reduction techniques.
Antithetic variates and systematic sampling, control variates, stratified sampling, importance sampling, Latin hypercube sampling, matching underlying assets..

Quasi-Monte Carlo methods.
Van der Corput sequence, Koksma-Hlawka bound, low-discrepancy sequences: Halton sequence, Faure sequence, and Sobol sequence, randomized quasi-Monte Carlo..

Application to Finance.
Valuation of exotic options, calculating VaR, stock price and interest rate modelling..

Assessment Breakdown
Continuous Assessment	50%	Examination Weight	50%

Course Work Breakdown
Type	Description	% of total	Assessment Date
Project	Programming the Monte Carlo method and an advanced Monte Carlo method for a given problem	50%	Sem 2 End

Reassessment Requirement
Resit arrangements are explained by the following categories; 1 = A resit is available for all components of the module 2 = No resit is available for 100% continuous assessment module 3 = No resit is available for the continuous assessment component
This module is category 3

Indicative Reading List

Paul Glasserman: 2004, Monte Carlo Methods in Financial Engineering, Springer, New York,
Ralf Korn, Elke Korn, and Gerald Kroisandt: 2010, Monte Carlo Methods and Models in Finance and Insurance, Taylor & Francis, Boca Raton,
Peter Jaeckel: 2005, Monte Carlo Method in Finance, Wiley & Sons Ltd, Chichester,
Søren Asmussen, Peter W. Glynn: 2007, Stochastic Simulation: Algorithms and Analysis, Springer, Berlin,
Harald Niederreiter: 1992, Random number generation and quasi-Monte Carlo methods, Society for Industrial and Applied Mathematics, Philadelphia,
Reuven Y. Rubinstein: 1981, Simulation and the Monte Carlo method, Wiley & Sons Ltd, New York,
J.M. Hammersley and D.C. Handscomb: 1964, Monte Carlo methods, Chapman and Hall, London,
Rüdiger Seydel: 2006, Tools for Computational Finance, 3. Edition, Springer, Berlin,
Desmond J. Higham: 2004, An Introduction to Financial Option Valuation, Cambridge University Press, Cambridge,