25833 Derivatives
UTS: Business: Finance and EconomicsCredit points: 6 cp
Subject level: Postgraduate
Result Type: Grade and marksHandbook description
This subject encourages students to investigate modelling asset price dynamics in discrete time and continuous time. Topics include, arbitrage pricing of derivatives in discrete and continuous time, different interpretations of the arbitrage pricing condition leading to the partial differential equation, martingale and integral evaluation viewpoints, and derivative pricing in both deterministic and stochastic interest rate environments.
Subject objectives/outcomes
On successful completion of this subject students should be able to:
- understand at an intuitive level discrete time and continuous time modelling of financial asset prices
- apply the principles of arbitrage pricing to derivative securities
- interpret derivative pricing relationships from various points of view
- implement basic derivative pricing models.
Contribution to graduate profile
This subject contributes to the overall aims of the course by introducing to students, in a mathematically simple setting, the basic arbitrage arguments underpinning the pricing of derivative instruments. The interpretation from both the partial differential equation and martingale viewpoints will both be emphasised. The basic notions of stochastic modelling of asset price dynamics will also be presented. Focus will be on developing an intuitive appreciation of the concepts presented. All of these concepts will be developed from a more sophisticated mathematical viewpoint in subsequent subjects.
Teaching and learning strategies
The subject will incorporate a range of strategies including lectures, assignment problems, and the use of a simulation package to illustrate certain key concepts.
Content
- Stochastic modelling of asset price movements
- Pricing derivatives in binomial trees
- The hedging argument in continuous time
- Derivative pricing via partial differential equations
- Martingale representation of derivative prices
- Integral representation of derivative prices
- A general framework for derivative security pricing
- Interest rate derivatives-the Vasicek approach
- Interest rate derivatives-the Heath, Jarrow and Morton approach.
Assessment
Assessment item 1: Assignment/Problems (Individual)
| Objective(s): | 1-3 |
| Weighting: | 20% |
| Task: | Individual assignment will be used to assess the ability of course participants to arrive at a sound understanding of financial markets using relevant financial techniques. These assignments will enable students to demonstrate that they have met objectives 1-3. |
Assessment item 2: Mid-Semester Examination (Individual)
| Objective(s): | 1-4 |
| Weighting: | 30% |
| Task: | Mid-semester examination will test students' knowledge and competencies in applying financial techniques to solve problems. It assures objectives 1-4. |
Assessment item 3: Final Examination (Individual)
| Objective(s): | 1-4 |
| Weighting: | 50% |
| Task: | The final examination will test students' knowledge and competencies in applying financial techniques to solve problems. It assures objectives 1-4. |
Indicative references
Lecture notes
The course will be based on the notes 'An Introduction to the Theory of Derivative Security Pricing; Techniques, Methods and Applications' by Carl Chiarella
Lecture slides
The printed lecture slides distributed to students are a copy of the lecture presentations.
Theory and computational problems
Theory and computational problems are included in the lecture notes at the end of each chapter.
Some additional problems may be distributed during the semester.
References
Bjork, T. (1998) Arbitrage Theory in Continuous Time, Oxford University Press.
Epps, T.W. (2000) Pricing Derivative Securities, World Scientific.
Lamberton, D. and Lapeyre, B. (1996) Introduction to Stochastic Calculus Applied to Finance, Chapman & Hall.
Neftci, S. N. (1996) An Introduction to the Mathematics of Financial Derivatives, Academic Press.
Wilmott, P. (1998) Derivatives, John Wiley & Sons.
Websites
www.asx.com.au (Australian Stock Exchange)www.sfe.com.au (Sydney Futures Exchange)
www.cbot.com (Chicago Board of Trade)
www.cme.com (Chicago Mercantile Exchange)
www.isda.org (International Swaps and Derivatives Association)
www.riskmetrics.com (RiskMetrics)
