Pricing perpetual options with stochastic discount interest rates |
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Authors: | Zhao Xia Zhang Bo |
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Institution: | (1) Institute of Finance, National Chiao Tung University, Hsinchu, Taiwan;(2) Department of Finance, Rutgers University, New Brunswick, NJ, USA;(3) Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan; |
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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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