This course introduces stochastic calculus based on Brownian motion and applies the theoretical concepts to finance, and especially, to option pricing within the Black-Scholes framework.
Stochastic ("Ito") calculus differs significantly from "ordinary" calculus because we want to integrate and differentiate with respect to the random Brownian motion process, which is not of bounded variation. It is essential for an understanding of the fundamental and advanced aspects of financial mathematics.
The course develops the basic concepts of:
- The Ito integral with an emphasis on martingales
- The Ito formula as a differentiation rule for stochastic processes
- The martingale representation theorem is derived
- The course continues with stochastic differential equations and develops the connection between them and "ordinary" partial differential equations.
- The modern finance theory of options pricing is developed and analysed using martingale methods and the techniques of stochastic integration theory.
- The renowned Black-Scholes formula is derived
- The course goes on to advanced options pricing techniques including a discussion of early exercise ("American") options.
Note: Graduate students attend joint classes with undergraduates but will be assessed separately.
Learning Outcomes
Upon successful completion, students will have the knowledge and skills to:
On successful completion of this course, students will be able to:
1. Explain the core mathematical tools and fundamental concepts of modern financial mathematics;
2. Solve a range of option pricing and hedging problems;
3. Apply the concepts of no arbitrage and risk minimisation in a range of quantitative finance contexts;
4. Demonstrate capabilities for advanced mathematical reasoning, analysis and modelling linked to the theory of stochastic processes.
Indicative Assessment
Assessment is expected to be based on:
- Assignments (50%; LO 1-4)
- Final examination (50%; LO 1-4)
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Requisite and Incompatibility
You will need to contact the Department of Mathematics to request a permission code to enrol in this course.
Fees
Tuition fees are for the academic year indicated at the top of the page.
If you are a domestic graduate coursework or international student you will be required to pay tuition fees. Tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.
- Student Contribution Band:
- 2
- Unit value:
- 6 units
If you are an undergraduate student and 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). You can find your student contribution amount for each course 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 |
|---|---|
| 2015 | $3096 |
- International fee paying students
| Year | Fee |
|---|---|
| 2015 | $4146 |
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 |
|---|---|---|---|---|---|---|
| 1907 | 20 Jul 2015 | 07 Aug 2015 | 31 Aug 2015 | 30 Oct 2015 | In Person | N/A |
