Applied Maths Seminar: Zhu -- Explicit Solution for Valuation of American Put Options

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
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