Registry

Module Specifications

Archived Version 2017 - 2018

Module Title
Module Code
School
Online Module Resources
NFQ level	8	Credit Rating	7.5
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

Description

This course is designed to give students strong practical and theoretical foundations in Monte Carlo methods with an emphasis on applications relevant to insurance and finance. Each week will consist of 2 hours of lectures/tutorials and 2 hours of computer labs. The emphasis will be on using mathematical theory to justify our approaches to solving practical programming problems which have real-world relevance. The primary applications for our methods will be frequency and severity pricing in insurance, interest rate modelling, and option pricing. Students are expected to know the statements of important results and interpret them but lengthy and technical proofs will not be required. Programming will be done in MATLAB; this is not primarily a coding module and the only requirement is that students write clear readable code.

Learning Outcomes

1. Apply basic results from probability theory to study the efficiency and appropriateness of Monte Carlo methods
2. Identify suitable methods for generating pseudorandom numbers
3. Use uniform random numbers to simulate random numbers of a given distribution
4. Analyse and interpret stochastic differential equations; approximate their solutions with appropriate discrete time processes for quantitative purposes
5. Write MATLAB code to simulate random variables and solutions to stochastic differential equations, empirically test pseudorandom number generators, and price options

*Type*	*Hours*	*Description*
Workload	Full-time hours per semester
Lecture	24	Lectures and Tutorials
Laboratory	24	Supervised computer laboratories
Independent Study	140	Self Study and Case Studies
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

Review of Probability Theory
Sigma-algebras, random variables, distribution functions, limit theorems, modes of convergence

Generating Random Numbers
Uniform random numbers, linear congruential generators, Chi-square and Kolmogorov-Smirnov tests, inverse transform method, acceptance rejection method

Introduction to the Monte Carlo Method
Strong law of large numbers, confidence intervals, error estimation

Introduction to Stochastic Differential Equations
Brownian motion – theory and simulation, motivation for SDEs, the Ito integral, Ito’s lemma, existence and uniqueness of solutions

Discretising and Simulating Stochastic Differential Equations
Euler-Maruyama and Milstein Schemes, strong and weak orders of convergence

Applications in Finance
Option pricing, interest rate modelling, frequency and severity pricing in insurance

Assessment Breakdown
Continuous Assessment	%	Examination Weight	%

Type	Description	% of total	Assessment Date
Course Work Breakdown

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
Unavailable

Indicative Reading List

P. Glasserman: 2013, Monte Carlo Methods in Financial Engineering, Springer Science and Business Media,

Other Resources

None

Programme or List of Programmes

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