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Approximate ordinary differential equations for the optimal exercise boundaries of American put and call options

Published online by Cambridge University Press:  15 August 2013

MARIANITO R. RODRIGO
MARIANITO R. RODRIGO*
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, New South Wales, Australia email: marianito_rodrigo@uow.edu.au
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Abstract

We revisit the American put and call option valuation problems. We derive analytical formulas for the option prices and approximate ordinary differential equations for the optimal exercise boundaries. Numerical simulations yield accurate option prices and comparable computational speeds when benchmarked against the binomial method for calculating option prices. Our approach is based on the Mellin transform and an adaptation of the Kármán–Pohlausen technique for boundary layers in fluid mechanics.

Keywords

American put and callFree boundary problemOptimal exercise boundaryBlack–Scholes kernelMellin transform
Type
Papers
Information
European Journal of Applied Mathematics , Volume 25 , Issue 1 , February 2014 , pp. 27 - 43
Copyright
Copyright © Cambridge University Press 2013 

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