Paul Johnson

Lecture Notes
Examples / Solutions
Reading List / Past Papers
Podcast/Forum/Feedback/FAQs

Lecture notes for the course will appear here on Mondays for the following week.

Examples and solutions for the course will appear here on Fridays.

Reading list for the course.

The Mathematics of Financial Derivatives

Wilmott, P., Howison, S., Dewynne, J., "The Mathematics of Financial Derivatives", Cambridge University Press, (1995) ISBN: 0521497892

Options, Futures and other Derivatives

Hull, J. C., 2011: "Options, Futures and other Derivatives", 8th edition, Prentice Hall. ISBN: 0132777428.

Please follow the link for podcasts of the lecture, the written additions to the notes will be recorded there. If you log onto Blackboard, the discussion forum can be found under the communication tab. If you are already logged in follow the link below. I will try to answer all queries from students on the forum, if you email me I will post the answer (anonymously) on the forum.

Blackboard Forum

Link to the Blackboard forum, make sure you are already logged in. To access it manually go to the communication tab on Blackboard and click on MATH20912. If you click to subcribe at the top you will be emailed when new posts appear on the forum.

Link

MATH20912 Podcasts

Link to your podcast portal, make sure you are already logged in.

Link

Brief Description

WARNING THIS IS ARCHIVE MATERIAL NO LONGER MAINTAINED -- This course is intended to serve as a basic introduction to financial mathematics.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.

Aims

The course 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.

Syllabus

Overview of basic concepts in securities markets.
Stochastic models for stock prices.
Hedging strategies and managing market risk using derivatives.
Binomial option pricing model.
Risk-neutral valuation, replication and pricing of contingent claims.
Black-Scholes analysis.
Interest rate models.

Intended Learning Outcomes

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 analytic formula to 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.

Department of Mathematics

ARCHIVE:: MATH20912: Introduction to Financial Mathematics

The Mathematics of Financial Derivatives

Options, Futures and other Derivatives

Blackboard Forum

MATH20912 Podcasts

MATH20912: The Mathematics of Financial Derivatives

MATH20912: Options, Futures and other Derivatives

MATH20912: Blackboard Forum

MATH20912: MATH20912 Podcasts