# module specification

## MA7008 - Financial Mathematics (2024/25)

Module specification Module approved to run in 2024/25
Module title Financial Mathematics
Module level Masters (07)
Credit rating for module 20
School School of Computing and Digital Media
Total study hours 200

 100 hours Guided independent study 48 hours Scheduled learning & teaching activities 52 hours Assessment Preparation / Delivery
Assessment components
Type Weighting Qualifying mark Description
In-Course Test 30%   Class Test (1 hour)
Coursework 70%   Case Study Report (2000 words)
Running in 2024/25

(Please note that module timeslots are subject to change)
Period Campus Day Time Module Leader
Autumn semester North Wednesday Afternoon

## Module summary

This module provides an introduction to some of the key mathematical methods used in financial calculations and how they are applied to the valuation of projects in the presence of uncertainty. There will be a particular focus on Discounted Cash Flow and Real Options methods but also on recent developments in the field of project valuation.

Methods such as Monte-Carlo simulation for financial options valuation and the Capital Asset Pricing Model (CAPM) with the aim of optimising a portfolio will also be explored using real financial data.

The module aims to:

1. Provide students with a set of up-to-date mathematical tools for project valuation with a particular focus on financial applications.

2. Provide a foundation in modern developments in optimisation theory and methods and introduce essential topics of unconstrained and constrained optimisation.

3. Explore the applications of Capital Asset Pricing models to problems involving decision making in modern portfolio management using real world financial data

## Syllabus

- Discounted cash flow (DCF) methods of project evaluation and use of these methods in the presence of uncertainty, taxation and inflation. (LO1)

- Statistical models of asset returns, Monte-Carlo methods and the Black-Scholes formula for vanilla options. (LO2,4-6)

- Recent developments in project valuation methods with a particular focus on methods of risk analysis such as value-at-risk. (LO3,4-6)

- The Capital Asset Pricing Models – both single and multifactor models such as the Fama and French three-factor model. (LO3,4-6)

- Lagrange methods for constrained and unconstrained optimisation problems. (LO3,4-6)

## Balance of independent study and scheduled teaching activity

The module will be delivered through a combination of lectures and associated tutorial and laboratory workshops over a period of 12 weeks. Topics of lectures will be supplemented with laboratory sessions to illustrate the application of the techniques studied. Computer-based software such as Excel and R will be used and students will be encouraged to broaden their knowledge by exploring complex real-world problems both systematically and creatively, and by critically evaluating the applicability of the techniques. The tutorial and lab sessions will also provide opportunities for students to obtain informal feedback from the teaching staff on their progress.
Additional teaching and learning resources will be made available via WebLearn and students will be expected to spend a significant proportion of their time on private study.

## Learning outcomes

On completing the module, students will be able to:

[LO1] Demonstrate systematic knowledge and understanding of Discounted Cash Flow (DCF) methods for project evaluation and use these methods in the presence of uncertainty, taxation and inflation
[LO2] Demonstrate a comprehensive understanding of Statistical models of asset returns, Monte-Carlo method and the Black-Scholes formula for a range of vanilla options valuation
[LO3] Apply knowledge and skills of mathematical concepts underlying the theory of nonlinear optimisation and apply the acquired skills to analyse portfolio optimisation problems independently
[LO4] Critically evaluate the practical usefulness and limitations of the techniques studied
[LO5] Use software for solving problem of moderate to large scale
[LO6] Carry out independent investigation and write clear and concise scientific reports

## Bibliography

Ross, S. A. and Westerfield, R. W. (2010) Modern Financial Management, 8th ed, McGraw-Hill.