• Offered by Department of Mathematics
  • ANU College ANU Joint Colleges of Science
  • Classification Advanced
    Specialist
  • Course subject Mathematics
  • Areas of interest Mathematics
  • Academic career PGRD
  • Course convener
    • Dr Dale Roberts
  • Mode of delivery In Person
  • Offered in Second Semester 2014
    See Future Offerings

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)

The ANU uses Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. While the use of Turnitin is not mandatory, the ANU highly recommends Turnitin is used by both teaching staff and students. For additional information regarding Turnitin please visit the ANU Online website.

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. Students continuing in their current program of study will have their tuition fees indexed annually from the year in which you commenced your program. 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
Domestic fee paying students
Year Fee
1994-2003 $1650
2004 $2160
2005 $2520
2006 $2520
2007 $2520
2008 $2916
2009 $2916
2010 $2916
2011 $2946
2012 $2946
2013 $2946
2014 $2946
International fee paying students
Year Fee
1994-2003 $2796
2004 $3618
2005 $3618
2006 $3618
2007 $3618
2008 $3618
2009 $3618
2010 $3750
2011 $3756
2012 $3756
2013 $3756
2014 $3762
Note: Please note that fee information is for current year only.

Offerings, Dates and Class Summary Links

The list of offerings for future years is indicative only.
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
7453 21 Jul 2014 08 Aug 2014 31 Aug 2014 30 Oct 2014 In Person N/A

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