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OPTIMAL EXERCISE PRICE OF AMERICAN OPTIONS NEAR EXPIRY

Part of: Asymptotic theory

Published online by Cambridge University Press:  02 June 2010

WEN-TING CHEN  and
SONG-PING ZHU
WEN-TING CHEN
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia (email: wc904@uow.edu.au, spz@uow.edu.au)
SONG-PING ZHU*
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia (email: wc904@uow.edu.au, spz@uow.edu.au)
*
✉For correspondence; e-mail: spz@uow.edu.au
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Abstract

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This paper investigates American puts on a dividend-paying underlying whose volatility is a function of both time and underlying asset price. The asymptotic behaviour of the critical price near expiry is deduced by means of singular perturbation methods. It turns out that if the underlying dividend is greater than the risk-free interest rate, the behaviour of the critical price is parabolic, otherwise an extra logarithmic factor appears, which is similar to the constant volatility case. The results of this paper complement numerical approaches used to calculate the option values and the optimal exercise price at times that are not close to expiry.

Keywords

singular perturbationAmerican put optionsoptimal exercise pricelocal volatility model

MSC classification

Secondary: 34E15: Singular perturbations, general theory
Type
Research Article
Information
The ANZIAM Journal , Volume 51 , Issue 2 , October 2009 , pp. 145 - 161
Copyright
Copyright © Australian Mathematical Society 2010

References

[1]Barles, G., Burdeau, J., Romano, M. and Samscen, N., “Critical stock price near expiration”, Math. Finance 5 (1995) 77–95.CrossRefGoogle Scholar
[2]Chevalier, E., “Critical price near maturity for an American option on a dividend-paying stock in a local volatility model”, Math. Finance 15 (2005) 439–463.CrossRefGoogle Scholar
[3]Evans, J. D., Kuske, R. and Keller, J. B., “American options on assets with dividends near expiry”, Math. Finance 12 (2002) 219–237.CrossRefGoogle Scholar
[4]Kirsch, A., Introduction to the mathematical theory of inverse problems (Springer, New York, 1996).CrossRefGoogle Scholar
[5]Zhao, J. and Wong, H. Y., “A closed-form solution to American options under general diffusion processes”, Quant. Finance, to appear, doi:10.1080/14697680903193405.CrossRefGoogle Scholar
[6]Zhu, S. P., “An exact and explicit solution for the valuation of American put options”, Quant. Finance 6 (2006) 229–242.CrossRefGoogle Scholar