Pricing perpetual options with stochastic discount interest rates

Pricing perpetual options with stochastic discount interest rates 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quality & Quantity Springer Journals

Pricing perpetual options with stochastic discount interest rates

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Publisher
Springer Netherlands
Copyright
Copyright © 2010 by Springer Science+Business Media B.V.
Subject
Social Sciences; Methodology of the Social Sciences; Social Sciences, general
ISSN
0033-5177
eISSN
1573-7845
D.O.I.
10.1007/s11135-010-9358-0
Publisher site
See Article on Publisher Site

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.

Journal

Quality & QuantitySpringer Journals

Published: Jul 30, 2010

References

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