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Peter Buchen
School of Mathematics & Statistics,
University of Sydney
Pricing Financial Derivatives with the Method of Images
Wednesday 5th March 14:05-14:55pm,
Eastern Avenue Lecture Theatre.
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.
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