Module: Simulation for Finance

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Module: Simulation for Finance

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Module Specifications

Academic Year 2026 - 2027

Module Title	Simulation for Finance
Module Code	MTH1077 (ITS: MS555)
Faculty	Science & Health	School	Mathematical Sciences
NFQ level	9	Credit Rating	7.5

Description

The module provides an introduction to the theory of Monte Carlo simulation, and gives nancial applications in the area of option pricing. The module includes substantial projects involving computer simulation in the MATLAB programming language. Prior familiarity with MATLAB is not assumed: sucient time is available in laboratories to acquaint students with the necessary code to complete the module. MS450M is aimed not only at masters students who have completed mathematical undergraduate pro- grammes, but also students who have completed undergraduate courses in other disciplines, including Engineering, Quantitative Finance and some elds of Science. MS450 is aimed at undergraduate students in both Actuarial Mathematics and in Financial Mathematics. The module neither requires a prior knowledge of, nor includes in its syllabus, stochastic calculus. Students are expected to attend lectures, tutorials, and tutor{supported laboratories. They will also engage in individual and group computer projects, facilitated by a tutor. Theoretical aspects of the course covered in lectures, as well as computational examples covered in tutorials, will be assessed by an end-of-semester examination.

Learning Outcomes

1. apply basic results from the limit theory of probability to determine the efficacy and efficiency of Monte Carlo simulations;
2. identify good methods for generating uniform pseudo random numbers. Understand the mathematical theory of Linear Congruential Generators in depth.
3. use uniform random numbers to simulate random numbers of a given distribution, including distri- butions of special importance in finance;
4. value various types of financial options using Monte Carlo simulation; quantify the quality of Monte Carlo estimators of derivative prices.
5. write MATLAB code to simulate random variables, empirically test pseudorandom number genera- tors, and price options. Avoid build-in routines from the Statistics Package in Matlab.

*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

Section Breakdown
CRN	11177	Part of Term	Semester 1
Coursework	50%	Examination Weight	50%
Grade Scale	40PASS	Pass Both Elements	N
Resit Category	RC1	Best Mark	N
Module Co-ordinator	Kwok Chuen Wong	Module Teacher	Emmet Lawless

Type	Description	% of total	Assessment Date
Assessment Breakdown
Project	Individual computer project	25%	Week 6
Project	Group computer project	35%	Week 6
Formal Examination	End-of-Semester Final Examination	40%	End-of-Semester

Reassessment Requirement Type
Resit arrangements are explained by the following categories; RC1: A resit is available for both^* components of the module. RC2: No resit is available for a 100% coursework module. RC3: No resit is available for the coursework component where there is a coursework and summative examination element. ^* ‘Both’ is used in the context of the module having a coursework/summative examination split; where the module is 100% coursework, there will also be a resit of the assessment

Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

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 MATLAB programming (in laboratories)

Introduction to Monte Carlo simulation
- Crude Monte Carlo simulation; the strong law of large numbers, Central Limit theorem, con- dence intervals, and their role. - Monte Carlo integration, error estimation.

Pseudorandom number generators
- Good properties. The linear congruential number generator. Tests for good LCG generators. - Empirical distribution function. Testing pseudorandom number generators using Chi-Square and Kolmogorov-Smirnov tests.

Generation of random variables
- Inverse transform method, acceptance rejection method. - Generation of important random variables (especially Poisson, exponential, double exponential, normal).

Variance of Monte Carlo methods
- Variance reduction using the method of covariates.

Simulation of European options
- Assuming stock prices are lognormally distributed, and returns are stationary and normally distributed. Option price is an expectation. - Comparison with Black-Scholes formula for call. Put prices via put-call parity. Empirical valuation: determination of condence intervals for value, use of variance reduction.

Simulation of path-dependent options
- Simulation of a path of (lognormally distributed) stock prices at discrete points. - Asian options, barrier options. Condence intervals.

Indicative Reading List

Books:

D. J. Higham: 2005, An Introduction to Financial Option Pricing, Cambridge University Press,,
H.Wang: 2012, Monte Carlo simulation with applications to finance, Taylor and Francis,
D. F. Griths: 0, An Introduction to MATLAB, Dundee Numerical Analysis Reports, http://www.maths.dundee.ac.uk/ftp/na-reports/MatlabNotes.pdf,

Articles:
None

Other Resources

None

This course MS555 is for the Master Level and thus distinguished from the Bachelor Course MS455 in four points (a) first individual case study is shorter than the one for MS555 (b) length of final exam (150 minutes instead of 120 minutes) (c) number of questions in final exam: Choose 3/4 exam questions instead of 4 questions (d) learning outcomes.

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