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25839 Mathematics of Finance

UTS: Business: Finance and Economics
Credit points: 6 cp

Subject level: Postgraduate

Result Type: Grade and marks

Requisite(s): 35365 Stochastic Calculus in Finance
There are also course requisites for this subject. See access conditions.

Handbook description

This subject introduces the theory of mathematical finance with applications in derivative pricing, portfolio optimisation and risk management. Techniques of no-arbitrage pricing in finance and financial mathematics are explored. Theoretical problems involving hedging derivatives and change of probability measures and portfolio optimisation are formulated and solved.

Subject objectives/outcomes

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

  1. define and illustrate the terms used in the study of financial mathematics including no-arbitrage pricing and hedging and portfolio optimisation
  2. demonstrate and apply techniques for derivative pricing in finance
  3. formulate and solve applied and theoretical problems involving hedging derivatives, change of probability measures and portfolio optimisation
  4. communicate clearly knowledge of the subject matter in financial contexts and solutions to the problems requiring such knowledge
  5. demonstrate preparedness to undertake further study in Numerical Methods of Finance.

Indicative references

Platen, E. and Heath, D. (2006) A Benchmark Approach to Quantitative Finance, Springer Finance, Springer Verlag, ISBN 3-540-26212-1

Baxter, M. and Rennie, A. (1996) Financial Calculus — An Introduction to Derivative Pricing, Cambridge University Press.

Elliott, R. J. and Kopp, P. E. (1995) Mathematics of Financial Markets, Springer-Verlag.

Korn, R. (1997) Optimal Portfolios, World Scientific.

Kloeden, P.E. and Platen, E. (1999) Numerical Solution of Stochastic Differential Equations, Vol 23 of Applied Math., Springer, Third corrected printing.

Neftci, S. N. (1996) In Introduction to the Mathematics of Financial Derivatives, Academic Press.

Lecture notes

The course will use the notes 'Mathematics of Finance' by Eckhard Platen.

Exercises

Exercises are included in the lecture notes at the end of each chapter. The solutions can be found in the monograph Platen and Heath (2006).

Websites

www.aimr.org (Association for Investment Management and Research)

www.asx.com.au (Australian Stock Exchange)

www.sfe.com.au (Sydney Futures Exchange)

www.cbot.com (Chicago Board of Trade)

www.adtrading.com (Applied Derivative Trading)

www.riskmetrics.com (RiskMetrics)