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Unit of study_

MATH4511: Arbitrage Pricing in Continuous Time

The aim of Financial Mathematics is to establish a theoretical background for building models of securities markets and provides computational techniques for pricing financial derivatives and risk assessment and mitigation. Specialists in Financial Mathematics are widely sought after by major investment banks, hedge funds and other, government and private, financial institutions worldwide. This course is foundational for honours and masters programs in Financial Mathematics. Its aim is to introduce the basic concepts and problems of securities markets and to develop theoretical frameworks and computational tools for pricing financial products and hedging the risk associated with them. This unit will focus on two ideas that are fundamental for Financial Mathematics. You will learn how the concept of arbitrage and the concept of martingale measure provide a unified approach to a large variety of seemingly unrelated problems arising in practice. You will also learn how to use the wide range of tools required by Financial Mathematics, including stochastic calculus, partial differential equations, optimisation and statistics. By doing this unit, you will learn how to formulate problems that arise in finance as mathematical problems and how to solve them using the concepts of arbitrage and martingale measure. You will also learn how to choose an appropriate computational method and devise explicit numerical algorithms useful for a practitioner.

Code MATH4511
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
Assumed knowledge:
Familiarity with basic probability (eg STAT2X11), with differential equations (eg MATH3X63, MATH3X78), achievement at credit level or above in MATH3XXX or STAT3XXX units or equivalent

At the completion of this unit, you should be able to:

  • LO1. Demonstrate a coherent and advanced knowledge of the concept of arbitrage and martingale measure and how they provide a unified approach to a wide variety of problems in finance
  • LO2. Formulate real-world financial problems in mathematical terms and determine the most suitable framework to analyse the resulting mathematical problem
  • LO3. Generate analytic and computational solutions to diverse problems of finance
  • LO4. Communicate mathematical analyses and solutions to mathematical and practical problems of financial mathematics clearly in a variety of media to diverse audiences
  • LO5. Take responsibility for their own learning by seeking out and using material from the research literature and elsewhere to extend their knowledge of methods of financial mathematics