This is an advanced course in derivatives pricing and hedging, and their applications. The aim is to cover topics such as: advanced features of the Black-Scholes model, including exotic options and derivatives dependent on the same Brownian motion; some bivariate/multivariate theory (normal distribution, Brownian motion in 2 dimensions), as needed for pricing options on correlated assets; Rubinstein's binomial pyramid for approximating a bivariate GBM; change of numeraire and equivalent martingale measures; optimal stopping theory as needed for American option pricing; hedging concepts in this context; alternatives to Black-Scholes models; local volatility models, jump diffusion and GARCH models. There will be an emphasis on early exercise options, and some time will be spent on the mathematical/stochastic foundations necessary for understanding these and other applications. Some Value-at-Risk concepts may be introduced, and applied to portfolios containing derivatives. Credit derivatives may also be discussed.
Learning Outcomes
Upon successful completion, students will have the knowledge and skills to:
- Use Brownian motion, martingales and Ito's formula.
- Use alternatives to Black-Scholes models such as local volatility, jump diffusion and GARCH models.
- Apply the arbitrage-free approach to the pricing of options, including exotic options, using the basic mathematical tools required, and demonstrate an understanding of how these options are used in financial practice.
- Value options on correlated assets, including the mathematical/stochastic foundations necessary.
- Demonstrate an understanding of the theory and use of early exercise options, including the use of optimal stopping theory.
Indicative Assessment
- Typical assessment may include, but is not restricted to: assignments and a final exam. (100) [LO 1,2,3,4,5]
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Workload
Students are expected to commit at least 10 hours per week to completing the work in this course. This will include at least 3 contact hours per week and up to 7 hours of private study time.
Inherent Requirements
Not applicable
Requisite and Incompatibility
Prescribed Texts
John Hull, Options Futures and Other Derivatives: Global Edition, 8e, 2012.
Risk Neutral Valuation, Bingham, N. and Kiesel, R., Springer, 2004.
Preliminary Reading
Intro. to Stochastic Calculus with Applications., F. Klebaner, Imp. Coll. Press, 1998.
Elementary Stochastic Calculus with Finance in View, T. Mikosch, World Scientific, 1998.
Financial Calculus, M.W. Baxter and A.J.O. Rennie, Cambridge Univ. Press, 1996.
Options Markets, J. C. Cox and Mark Rubinstein, Prentice-Hall, 1985.
Levy Processes in Finance: Pricing Financial Derivatives, W. Schoutens, Wiley, 2003.
Option Valuation, R. Gibson, McGraw-Hill, 1991
Financial Derivatives, R. W. Cobb, Blackwell, 1996.
Derivative Securities, R. Jarrow and S. Turnbull, Thomson Learning, 2000.
Value at Risk: the New Benchmark for Managing Financial Risk, P. Jorion, 2nd Ed., New York: McGraw-Hill, 2001.
Fees
Tuition fees are for the academic year indicated at the top of the page.
Commonwealth Support (CSP) Students
If you have been offered a Commonwealth supported place, your fees are set by the Australian Government for each course. At ANU 1 EFTSL is 48 units (normally 8 x 6-unit courses). More information about your student contribution amount for each course at Fees.
- Student Contribution Band:
- 34
- Unit value:
- 6 units
If you are a domestic graduate coursework student with a Domestic Tuition Fee (DTF) place or international student you will be required to pay course tuition fees (see below). Course tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.
Where there is a unit range displayed for this course, not all unit options below may be available.
| Units | EFTSL |
|---|---|
| 6.00 | 0.12500 |
Course fees
- Domestic fee paying students
| Year | Fee |
|---|---|
| 2024 | $4680 |
- International fee paying students
| Year | Fee |
|---|---|
| 2024 | $6000 |
Offerings, Dates and Class Summary Links
ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage.
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.
Second Semester
| Class number | Class start date | Last day to enrol | Census date | Class end date | Mode Of Delivery | Class Summary |
|---|---|---|---|---|---|---|
| 8488 | 22 Jul 2024 | 29 Jul 2024 | 31 Aug 2024 | 25 Oct 2024 | In Person | N/A |
