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Some mathematical results in the pricing of American options

Published online by Cambridge University Press:  26 September 2008

J. N. Dewynne ,
S. D. Howison ,
I. Rupf  and
P. Wilmott
J. N. Dewynne
Affiliation:
Department of Mathematics, University of Southampton, Southampton S09 5NH, UK
S. D. Howison
Affiliation:
Mathematical Institute, 24–29 St Giles, Oxford 0X1 3LB, UK
I. Rupf
Affiliation:
Mathematical Institute, 24–29 St Giles, Oxford 0X1 3LB, UK
P. Wilmott
Affiliation:
Mathematical Institute, 24–29 St Giles, Oxford 0X1 3LB, UK
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Abstract

We examine the Black–Scholes partial differential equation for the pricing of a traded option (an American call option on an asset paying a continuous dividend) and make comparisons with other well known free boundary diffusion problems, such as the oxygen consumption problem. The pricing of American options can be viewed as a free boundary problem and is, therefore, inherently nonlinear. We consider the short and long time behaviour of the free boundary, present analytic results for the option value in such limits, and consider the formulation of the problem as a variational inequality, and its numerical solution.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 4 , Issue 4 , December 1993 , pp. 381 - 398
Copyright
Copyright © Cambridge University Press 1993

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