Module: Simulation for Finance

Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

Module Title	Simulation for Finance
Module Code	MS455 (ITS) / MTH1065 (Banner)
Faculty	Science & Health	School	Mathematical Sciences
Module Co-ordinator	Emmet Lawless
Module Teachers	John Appleby, Kwok Chuen Wong
NFQ level	8	Credit Rating	7.5
Pre-requisite	Not Available
Co-requisite	Not Available
Compatibles	Not Available
Incompatibles	Not Available

Repeat the module

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. This module covers practical parts for the topic "Stochastic Processes" from the IFoA subject CS2. 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 R; 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 R code to simulate random variables and solutions to stochastic differential equations, empirically test pseudorandom number generators, and price options
6. Write R code to simulate Markov processes to perform applications in finance and insurance
7. Apply the theory of the Markov process to practical tasks in insurance and finance

*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, applications to Markov chains and jump processes

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	50%	Examination Weight	50%

Type	Description	% of total	Assessment Date
Course Work Breakdown
Group project	Group Project on Random Number Generation, Monte Carlo method	15%	Week 6
Group project	Group Project on Option Pricing	15%	Week 11
Practical/skills evaluation	2-hour Lab exam in R simulation for Markov processes with applications in finance and insurance	20%	Week 12

Reassessment Requirement Type
Resit arrangements are explained by the following categories: Resit category 1: A resit is available for both* components of the module. Resit category 2: No resit is available for a 100% continuous assessment module. Resit category 3: No resit is available for the continuous assessment component where there is a continuous assessment and examination element.
* ‘Both’ is used in the context of the module having a Continuous Assessment/Examination split; where the module is 100% continuous assessment, there will also be a resit of the assessment
This module is category 1

Indicative Reading List

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

Other Resources

None

MS455 is for the Bachelor level students and is distinguished from the (Masters level course) MS555 in the end-of-semester assessment: MS555 students are presented with longer and more challenging questions which test their depth of knowledge more rigorously.