Mathematics of Finance III

This subject is not offered in 2014.

Estimated total time commitment of 120 hours per semester

ACTL90001 Mathematics of Finance I

None

Students should be competent in the use of Excel.

ACTL40004 Advanced Financial Mathematics I

For the purposes of considering requests for Reasonable Adjustments under the Disability Standards for Education (Cwth 2005), and Students Experiencing Academic Disadvantage Policy, academic requirements for this subject are articulated in the Subject Description, Subject Objectives, Generic Skills and Assessment Requirements for this entry.

The University is dedicated to provide support to those with special requirements. Further details on the disability support scheme can be found at the Disability Liaison Unit website: http://www.services.unimelb.edu.au/disability/

The binomial model; risk-neutral pricing of derivative securities; introduction to Ito's formula and SDEs; stochastic asset models; Black-Scholes model; arbitrage and hedging; interest-rate models; actuarial applications.

On successful completion of this subject a student should be able to:

• Demonstrate a knowledge of the properties of option prices, valuation methods and hedging techniques, and be able to apply these;
• Show how to use binomial trees and lattices in valuing options;
• Apply the Ito calculus;
• Derive option prices under the Black-Scholes model;
• Describe and apply in simple models, including the binomial model and the Black-Scholes model, the approach to pricing using deflators and demonstrate its equivalence to the risk-neutral pricing approach;
• Demonstrate a knowledge of models of the term structure of interest rates;
• Describe, as a computational tool, the risk-neutral approach to the pricing of zero coupon bonds and interest-rate derivatives for a general one-factor diffusion model for the risk-free rate of interest;
• Demonstrate a knowledge of simple models for credit risk.

• A 1000 word assignment due second half of semester (10%);
• A one hour mid-semester test (20%) and
• Two hour end of semester exam (70%).

You will be advised of prescribed texts by your lecturer.

This subject is not available as a breadth subject.

High level of development:

• Written communication;
• Problem solving;
• Mathematical reasoning;
• Simple models of credit risk;
• Application of theory to practice;
• Interpretation and analysis.