MATH4431 Advanced Option Pricing
For further information about this unit, contact the Head of the Applied Mathematics Teaching Division, Dr Dave Galloway.
Further information about the School's Financial Mathematics program can be obtained from the Financial Mathematics Web Page.
An important and large part of modern quantitative finance is concerned with the valuation of derivative securities including not only vanilla calls and puts but also the vast family of exotic options. The latter includes barrier options, lookback options, compound options, American options, Asian options, rainbow options, credit derivatives and many others.
This unit develops a none-too-technical mathematical framework for obtaining the fair or arbitrage-free prices of such derivative securities. This framework includes the two main approaches in popular use: the risk-neutral expectations method and the corresponding PDE method. Students will be introduced to the necessary stochastic calculus methods that underlie both approaches. Some computational methods employed in industry will also be discussed.
While a good understanding of mathematical statistics and PDE's would be an advantage, the unit assumes neither. Thus students and practitioners with strong analytical skills will still benefit from this unit, regarded as one of the most advanced academic programs of its kind in the country.
Assumed knowledge: BSc in mathematics or equivalent, and familiarity with financial concepts such as arbitrage, options, and the basics of Black-Scholes option-pricing methodology.
Method of assessment: 60% from final exam, 40% from assignments.
Workload: 6 credit points (one eighth of the standard annual load for a full-time student).
Contact hours: twelve 2-hour lectures plus twelve hours of supervised work at times to be arranged.