SHOULD AN AMERICAN OPTION BE EXERCISED EARLIER OR LATER IF VOLATILITY IS NOT ASSUMED TO BE A CONSTANT?

Song-Ping Zhu () and Wen-Ting Chen ()
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Song-Ping Zhu: School of Mathematics and Applied Statistics, University of Wollongong NSW 2522, Australia
Wen-Ting Chen: School of Mathematics and Applied Statistics, University of Wollongong NSW 2522, Australia

International Journal of Theoretical and Applied Finance (IJTAF), 2011, vol. 14, issue 08, 1279-1297

Abstract: In this paper, we present a correction to Merton (1973)'s well-known classical case of pricing perpetual American put options by considering the same pricing problem under a stochastic volatility model with the assumption that the volatility is slowly varying. Two analytic formulae for the option price and the optimal exercise price of a perpetual American put option are derived, respectively. Upon comparing the results obtained from our analytic approximations with those calculated by a spectral collocation method, it is shown that our current approximation formulae provide fast and reasonably accurate numerical values of both option price and the optimal exercise price of a perpetual American put option, within the validity of the assumption we have made for the asymptotic expansion. We shall also show that the range of applicability of our formulae is remarkably wider than it was initially aimed for, after the original assumption on the order of the "volatility of volatility" being somewhat relaxed. Based on the newly-derived formulae, the quantitative effect of the stochastic volatility on the optimal exercise strategy of a perpetual American put option has also been discussed. A most noticeable and interesting result is that there is a special cut-off value for the spot variance, below which a perpetual American put option priced under the Heston model should be held longer than the case of the same option priced under the traditional Black-Scholes model, when the price of the underlying is falling.

Keywords: Perturbation method; perpetual American put options; Heston model (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (3)

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DOI: 10.1142/S0219024911006851

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