Type: Seminar

Distribution: World

Expiry: 5 Mar 2008

Auth: wm@p6283.pc.maths.usyd.edu.au

Vanilla options belong to the class of path-independent derivatives and are most conveniently priced using discounted risk-neutral expectation of the maturity payoff. Many exotic options including barrier and lookback options however, belong to the class of path-dependent derivatives. These latter options are more easily priced using PDE methods. This seminar summarises the research of the author and his students on the problem of pricing such path-dependent options in the classical Black-Scholes framework. In particular, we show how the path dependency can be eliminated using the Method of Images, reducing the problem to pricing an equivalent vanilla option. Illustrative examples include pricing barrier options, lookback options and double-barrier options all of which use the Method of Images for absorbing boundaries. We conclude the seminar by pricing a real estate lease, the only known financial example to us of a reflecting boundary problem.