Type: Seminar

Distribution: World

Expiry: 15 Mar 2007

Auth: philip@pisa.maths.usyd.edu.au

APPLIED MATHEMATICS SEMINAR AT THE UNIVERSITY OF SYDNEY Speaker: Assoc/Prof Song-Ping Zhu, University of Wollongong Title: An Exact and Explicit Solution for the Valuation of American Put Options DATE: Thursday, March 15 TIME: 3:00pm LOCATION: University of Sydney, Carslaw Building Room 375 Abstract: In this talk, an exact and explicit solution of the well-known Black-Scholes (1973) equation for the valuation of American put options is presented for the first time. To the author’s best knowledge, never has an exact and explicit formula been found for the valuation of American options of finite maturity, although there have been quite a few approximate solutions and numerical approaches proposed. The exact solution presented here is written in the form of a Taylor’s series expansion, which is constructed based on the homotopy-analysis method. The optimal exercise boundary, which forms the key difficulty of this highly nonlinear problem, has been elegantly and temporarily removed in the solution process, and consequently, the solution of a set of infinitely many linear problems can be analytically worked out at each order, resulting in a completely analytical and exact series-expansion solution for the optimal exercise boundary and the option price of American put options. The newly found analytical solution is also explicit as the optimal exercise boundary as well as the option price can be written as explicit functions of the risk-free interest rate, the volatility and the time to expiration. http://www.maths.usyd.edu.au/u/AppliedSeminar ------------------------------------------------------------------------