Financial Mathematics

Duration

Two Weeks, Period 2 (following Stochastic Calculus)

Lecturer

David Colwell (School of Banking & Finance, University of New South Wales)

Consultation Hours

Consult lecturer

Assessment

Final exam in last lecture (Friday 9 January, 4–6pm in Carslaw Room 275)

Assumed Knowledge

Stochastic Calculus

Course Outline

This module will consider the pricing and hedging of financial derivatives from a mathematical viewpoint. In particular, the topics covered will include:

• Mathematical model of the underlying financial market.
• Absence of arbitrage and market completeness.
• Probabilistic approach to pricing and hedging contingent claims under the Black-Scholes framework.
• Pricing and hedging contingent claims under stochastic volatility, and in incomplete markets in general.
• Traditional short rate models.
• Heath, Jarrow, and Morton framework for term structure modelling.
• Term structure models with finite dimensional realisations.
• Brace, Gatarek, and Musiela model.