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Pricing perpetual options with stochastic discount interest rates

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Abstract

The aim of this study is to investigate the prices and optimal exercise strategies of certain perpetual American options on the asset under stochastic discount interest model. This is different from Gerber and Shiu (N Am Actuar J 2(3):101–112, 1998), in which the interest force was a constant; here we suppose that the accumulated interest function is perturbed by the standard Brownian motion and Poisson process. We obtain an explicit expression of optimal option-exercise boundary in the case of perpetual put option. Moreover, we get a corresponding result when the individual claim is described by an exponential distribution. Finally, we analyze the influence of certain coefficients in stochastic interest model on the optimal option-exercise boundary.

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Authors and Affiliations

  1. Institute of Statistics and Actuary and School of Statistics and Mathematics, Shandong Economic University, 250014, Jinan, Shandong, People’s Republic of China

    Xia Zhao

  2. Center for Applied Statistics and School of Statistics, Renmin University of China, 100872, Beijing, People’s Republic of China

    Bo Zhang

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  1. Xia Zhao
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  2. Bo Zhang
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Correspondence to Bo Zhang.

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Zhao, X., Zhang, B. Pricing perpetual options with stochastic discount interest rates. Qual Quant 46, 341–349 (2012). https://doi.org/10.1007/s11135-010-9358-0

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  • DOI: https://doi.org/10.1007/s11135-010-9358-0

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