MPhys Physics with Astrophysics

This course is intended to serve as a basic introduction to financial mathematics. It gives a mathematical perspective on the valuation of financial instruments (futures, options, etc.) and their risk-management. The purpose of the course is to introduce students to the stochastic techniques employed in derivative pricing.

The course unit unit aims to enable students to acquire active knowledge and understanding of some basic concepts in financial mathematics including stochastic models for stocks and pricing of contingent claims.

On completion of this unit successful students will be able to: 

• Compare the value of standard financial contracts such as stocks, bonds and options at different times using a risk-free discount factor.
• Calculate the expected value of a portfolio under a subjective probability measure.
• Sketch payoff diagrams for a variety of portfolios, and be able to predict what the effect of changing the portfolio will be.
• Construct no-arbitrage arguments to derive upper and lower bounds of financial contracts and exploit arbitrage opportunities.
• Construct hedging arguments for the discrete one-step binomial model and the continuous Black-Scholes model.
• Calculate the expected value of a financial contract under the risk-neutral measure using a binomial-tree.
• Derive the analytic formula and perform analysis on both the value and the ‘Greeks’ of a financial contract.
• Derive the analytic formula for a bond with coupons, and perform analysis on the value of the financial contract.

1.Overview of basic concepts in securities markets.

2.Stochastic models for stock prices.

3.Hedging strategies and managing market risk using derivatives.

4.Binomial option pricing model.

5.Risk-neutral valuation, replication and pricing of contingent claims.

6.Black-Scholes analysis.

7.Interest rate models.

• Coursework; Weighting within unit 20%
• End of semester examination; Weighting within unit 80%

Feedback tutorials will provide an opportunity for students' work to be discussed and provide feedback on their understanding.  Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback.  Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.

• J. Hull, Options, Futures and Other Derivatives, 7th Edition, Prentice-Hall, 2008.
• P. Wilmott, S. Howison and J. Dewynne, The Mathematics of Financial Derivatives: A Student Introduction, Cambridge University Press, 1995

The independent study hours will normally comprise the following. During each week of the taught part of the semester:

• You will normally have approximately 60-75 minutes of video content. Normally you would spend approximately 2-2.5 hrs per week studying this content independently
• You will normally have exercise or problem sheets, on which you might spend approximately 1.5hrs per week
• There may be other tasks assigned to you on Blackboard, for example short quizzes or short-answer formative exercises
• In some weeks you may be preparing coursework or revising for mid-semester tests
   

Together with the timetabled classes, you should be spending approximately 6 hours per week on this course unit.

The remaining independent study time comprises revision for and taking the end-of-semester assessment.