Financial Mathematics

Two Weeks, Period 2 (following Stochastic Calculus)
David Colwell (School of Banking & Finance, University of New South Wales)
Consultation Hours
Consult lecturer
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.