25923 Derivative Security Pricing

Subject level: Undergraduate

Handbook description

This subject provides the techniques needed to analyse and price derivative securities and to understand some of the key associated quantitative arguments. Topics include: derivative securities; arbitrage arguments; geometric Brownian motion model of asset prices; Ito's lemma; risk-neutral pricing; Black Scholes option pricing model; currency, index and futures options; hedging techniques; and interest rate derivative securities.

Subject objectives/outcomes

On successful completion of this subject, students should be able to:

1. understand the concepts used in the modern approach to derivative pricing
2. apply the various concepts to perform explicit computations to price and hedge derivative securities. For example, application of Itô's lemma, change of measure, etc
3. construct models for derivatives and apply numerical techniques to compute their prices. For example, build binomial trees; apply Monte Carlo simulation techniques, etc.

Contribution to graduate profile

Derivative security pricing is a subject that provides a rigorous introduction to the modern theory of derivative pricing, with particular focus on the discrete time model for simplicity. The important mathematical concepts will be motivated with financial applications in mind. The subject will consider the theoretical models used for pricing financial derivatives and the common numerical techniques used to compute their values when closed form solutions are unavailable. Particular attention will be given to the Black/Scholes option pricing framework and the Cox/Ross/Rubinstein binomial tree approach to option pricing. This course has a strong quantitative and computational focus, and the students are expected to develop a good intuitive understanding of the various concepts by experimenting with the theoretical models and solution techniques.

Teaching and learning strategies

This subject is presented in a three hour combined lecture and tutorial session once per week, and fulfils the aims and principles of the UTS flexible learning strategy, which is to provide students with flexible options about how, when and where they learn. Attendance at lectures is not compulsory. However the content of the subject and the assessment is based on the assumption that the students will attend all classes.

Content

• Key ideas illustrated in a binomial setting.
• The Black/Scholes model and the associated quantitative methods.
• Implied volatility and calibration to market prices.
• The term structure of interest rates.
• Introducing interest rate risk.
• Modelling interest rate risk in continuous time.
• Credit risk, credit derivatives and credit risk modelling.

Assessment

Assessment item 1: Two Assignments (Individual)

Assessment item 2: Final Examination (Individual)

Indicative references

Paul Wilmott, Jeff Dewynne & Sam Howison, Option Pricing: mathematical models and techniques, Oxford Financial Press, ISBN 0 9522082 0 2

Paul Wilmott, Sam Howison & Jeff Dewynne, The Mathematics of Financial Derivatives, Cambridge University Press, ISBN 0 521 49789 2

J.C. Hull, Options, Futures and Other Derivatives (4th Edition), Prentice Hall, ISBN 0 13 015822 4

Paul Wilmott, Paul Wilmott introduces Quantitative Finance, John Wiley, ISBN 0 471 49862 9

A. Etheridge, A course in Financial Calculus, Cambridge University Press, 0 521 89077 2

M. Baxter & A. Rennie, Financial Calculus, Cambridge University Press, 0 521 55289 3

N. Neftci, An introduction to the Mathematics of Financial Derivatives, Academic Press, 0 12 515390 2

R.C. Merton, Continuous Time Finance, Blackwell, 0 631 18508 9

Lecture slides

Printed version of the slides used during the lectures will be handed out at the beginning of each lecture. If for any reason you are not able to attend a class, then you should log onto UTSOnline and download an electronic version of the lecture notes for the class you have missed, or alternatively contact the lecturer by email.