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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 MS551M
School School of Mathematics
Online Module Resources

Module Co-ordinatorSemester 1: Olaf Menkens
Semester 2: Olaf Menkens
Autumn: Olaf Menkens
Module TeacherOlaf Menkens
NFQ level 8 Credit Rating 0
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 and implement various random numbers, random variables, and 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. Apply the Monte Carlo method to specific problems and optimise the simulation (minimise speed/error) using advanced Monte Carlo Methods.
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



Workload Full-time hours per semester
Type Hours Description
Lecture36No Description
Lab12Computer Lab
Independent learning140No 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
Introducing 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.
Linear congruential generator, inverse transformation method, 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, 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, randomized quasi-Monte Carlo..

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

Assessment Breakdown
Continuous Assessment50% Examination Weight50%
Course Work Breakdown
TypeDescription% of totalAssessment Date
ProjectProgramming the Monte Carlo method and an advanced Monte Carlo method for a given problem50%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,
  • Peter Jaeckel: 2005, Monte Carlo Method in Finance, Wiley & Sons Ltd, Chichester,
  • Desmond J. Higham: 2004, An Introduction to Financial Option Valuation, Cambridge University Press, Cambridge,
  • 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,
Other Resources
None
Array
Programme or List of Programmes
MFMMSc in Financial Mathematics
Timetable this semester: Timetable for MS551M
Date of Last Revision22-AUG-08
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