Optimal exercise price of American options near expiry

Wen-Ting Chen, Song-Ping Zhu

Abstract


This paper investigates American puts on a dividend-paying underlying whose volatility is a function of both time and underlying asset price. The asymptotic behavior 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 behavior 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.

doi:10.1017/S1446181110000052

Keywords


singular perturbation, American put options, optimal exercise price, local volatility model



DOI: http://dx.doi.org/10.21914/anziamj.v51i0.2302



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.