• Offered by Department of Mathematics
• ANU College ANU Joint Colleges of Science
• Course subject Mathematics
• Areas of interest Mathematics
• Academic career UGRD
• Course convener
• Dr Dale Roberts
• Mode of delivery In Person
• Co-taught Course
• Offered in Second Semester 2014
Mathematics of Finance (MATH3015)

This course provides an introduction to the theory of stochastic processes and its application in the mathematical finance area.

The course starts with background material on markets, modelling assumptions, types of securities and traders, arbitrage and risk minimisation. Basic tools needed from measure and probability, conditional expectations, independent random variables and modes of convergence are explained. Discrete and continuous time stochastic processes including Markov, Gaussian and diffusion processes are introduced. Some key material on stochastic integration, the theory of martingales, the Ito formula, martingale representations and measure transformations are described. The well-known Black-Scholes option pricing formula based on geometric Brownian motion is derived. Pricing and hedging for standard vanilla options is presented. Hedge simulations are used to illustrate the basic principles of no-arbitrage pricing and risk-neutral valuation. Pricing for some other exotic options such as barrier options are discussed. The course goes on to explore the links between financial mathematics and quantitative finance. Results which show that the transition densities for diffusion processes satisfy certain partial differential equations are presented. The course concludes with treatment of some other quantitative methods including analytic approximations, Monte Carlo techniques, and tree or lattice methods.

Mathematics of Finance provides an accessible but mathematically rigorous introduction to financial mathematics and quantitative finance. The course provides a sound foundation for progress to honours and post-graduate courses in these or related areas.

Note: This is an Honours Pathway Course. It continues the development of sophisticated mathematical techniques and their application begun in MATH3029 or MATH3320.

## 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 will 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

To enrol in this course you must have successfully completed MATH3029 or MATH3320.

## 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

## Course fees

Domestic fee paying students
Year Fee Description
1994-2003 \$1650
2014 \$2946
2013 \$2946
2012 \$2946
2011 \$2946
2010 \$2916
2009 \$2916
2008 \$2916
2007 \$2520
2006 \$2520
2005 \$2298
2004 \$1926
International fee paying students
Year Fee
1994-2003 \$3390
2014 \$3762
2013 \$3756
2012 \$3756
2011 \$3756
2010 \$3750
2009 \$3618
2008 \$3618
2007 \$3618
2006 \$3618
2005 \$3450
2004 \$3450
Note: Please note that fee information is for current year only.

## 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.

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
9271 21 Jul 2014 01 Aug 2014 31 Aug 2014 31 Oct 2014 In Person N/A

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