MA7008 - Financial Mathematics (2020/21)
|Module specification||Module approved to run in 2020/21|
|Module title||Financial Mathematics|
|Module level||Masters (07)|
|Credit rating for module||20|
|School||School of Computing and Digital Media|
|Total study hours||200|
|Running in 2020/21||
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.
1. To provide students with a set of up-to-date mathematical tools for project valuation with a particular focus on financial applications.
2. To provide a foundation in modern developments in optimisation theory and methods and introduce essential topics of unconstrained and constrained optimisation.
3. To explore the applications of Capital Asset Pricing models to problems involving decision making in modern portfolio management using real world financial data.
4. To equip students with sound knowledge of Monte-Carlo simulation analysis and its application to valuation of vanilla options.
- Discounted cash flow (DCF) methods of project evaluation and use of these methods in the presence of uncertainty, taxation and inflation.
- Statistical models of asset returns, Monte-Carlo methods and the Black-Scholes formula for vanilla options.
- Recent developments in project valuation methods with a particular focus on methods of risk analysis such as value-at-risk.
- The Capital Asset Pricing Models – both single and multifactor models such as the Fama and French three-factor model.
- Lagrange methods for constrained and unconstrained optimisation problems.
Learning and teaching
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 MATLAB 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.
On completing the module, students will be able to:
1. Demonstrate good knowledge and understanding of Discounted Cash Flow (DCF) methods for project evaluation and use these methods in the presence of uncertainty, taxation and inflation.
2. Demonstrate a good understanding of Statistical models of asset returns, Monte-Carlo method and the Black-Scholes formula for a range of vanilla options valuation.
3. Demonstrate good knowledge and understanding of mathematical concepts underlying the theory of nonlinear optimisation and apply the acquired skills to analyse portfolio optimisation problems.
4. Critically evaluate the practical usefulness and limitations of the techniques studied.
5. Use software for solving problem of moderate to large scale.
6. Carry out independent investigation and write clear and concise scientific reports.
Due to its practical nature, the module will be assessed by means of a one-hour class test and a comprehensive case study investigation. The case study investigation will involve analyses of a realistic problem and provides an opportunity for students to demonstrate their skills in the following activities in the form of an interim report and a structured final report.
- Preliminary investigation concerning the problem in hand.
- Selecting suitable methods for solving the problem.
- Evaluating the limitation of the techniques and the impact of any simplifying assumptions on the validity of the solution.
- Gathering input data and using software for analyses.
- Interpreting the results and writing a comprehensive report of about 2000 words.
The unseen class test will enable students to demonstrate their knowledge and understanding of the techniques covered in the first few weeks of the course.
Ross, S. A. and Westerfield, R. W. (2010) Modern Financial Management, 8th ed, McGraw-Hill.
Wilmott, P. (2006) Paul Wilmott Introduces Quantitative Finance, 2nd ed, Wiley. [CORE]
Higham, D. J. (2005) An Introduction to Financial Option Valuation, Cambridge.
Bernd A. B. (2004) Markov Chain Monte Carlo Simulations and Their Statistical Analysis, Singapore, World Scientific.