Faculty of Business: Finance and Economics
Credit points: 6 cp

Subject level: Undergraduate

Result Type: Grade and marks

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

Two Assignments (Individual)	40%
The two assignments are each worth 20% and will have theoretical and computational components, as well as a computer project component that will require work in Excel/VBA. These assignments reflect the practical and applied nature of the course and assure objectives 1-3.
Final Examination (Individual)	60%
Although the examination will mostly be computational in nature, the students will be expected to demonstrate their understanding of the theoretical aspects of the course, testing learning objectives 1-3.

Examinations will be conducted under University examination conditions, and hence thoroughly address concerns regarding secure assessment. The assignments will be secured through a combination of updating of assessment tasks across semesters and/or plagiarism detection software.

Indicative references

Bingham, N.H. and R. Kiesel. (1998). Risk–Neutral Valuation: Pricing and Hedging of Financial Derivatives. Springer Verlag, ISBN 1852330015.

Brigo, D. and F. Mercurio (2001). Interest Rate Models. Springer Verlag, ISBN 3540417729.

Jäckel, P. (2002). Monte Carlo Methods in Finance. John Wiley and Sons, ISBN 047149741X.

Jackson, M. and M. Staunton (2001). Advanced Modelling in Finance Using Excel and VBA. John Wiley and Sons, ISBN 0471499226.

Mikosch, T. (1998). Elementary Stochastic Calculus with Finance in View. World Scientific, ISBN 9810235437.

Schönbucher, P.J. (2003). Credit Derivatives Pricing Models: Models, Pricing and Implementation. John Wiley and Sons, ISBN 0470842911.