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The perpetual American put option for jump-diffusions with applications

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  • Aase, Knut K.

    (Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration)

Abstract

In this paper we solve an optimal stopping problem with an infinite time horizon, when the state variable follows a jump-diffusion. Under certain conditions our solution can be interpreted as the price of an American perpetual put option, when the underlying asset follows this type of process. We present several examples demonstrating when the solution can be interpreted as a perpetual put price. This takes us into a study of how to risk adjust jump-diffusions. One key observation is that the probability distribution under the risk adjusted measure depends on the equity premium, which is not the case for the standard, continuous version. This difference may be utilized to find intertemporal, equilibrium equity premiums, for example. Our basic solution is exact only when jump sizes can not be negative. We investigate when our solution is an approximation also for negative jumps. Various market models are studied at an increasing level of complexity, ending with the incomplete model in the last part of the paper.

Suggested Citation

  • Aase, Knut K., 2005. "The perpetual American put option for jump-diffusions with applications," Discussion Papers 2005/12, Norwegian School of Economics, Department of Business and Management Science.
    • Handle: RePEc:hhs:nhhfms:2005_012
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    File URL: http://hdl.handle.net/11250/163574
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    References listed on IDEAS

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    1. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    2. Aase, Knut K., 2005. "Using Option Pricing Theory to Infer About Equity Premiums," Discussion Papers 2005/11, Norwegian School of Economics, Department of Business and Management Science.
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    14. Campbell, John Y, 1993. "Intertemporal Asset Pricing without Consumption Data," American Economic Review, American Economic Association, vol. 83(3), pages 487-512, June.
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    18. Ernesto Mordecki, 2002. "Optimal stopping and perpetual options for Lévy processes," Finance and Stochastics, Springer, vol. 6(4), pages 473-493.
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    Cited by:

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    2. Armerin, Fredrik, 2023. "Investments with declining cost following a Lévy process," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1052-1062.
    3. Armerin, Fredrik, 2020. "Investments with declining cost following a Lévy process," Working Paper Series 20/14, Royal Institute of Technology, Department of Real Estate and Construction Management & Banking and Finance.
    4. Marzia De Donno & Zbigniew Palmowski & Joanna Tumilewicz, 2020. "Double continuation regions for American and Swing options with negative discount rate in Lévy models," Mathematical Finance, Wiley Blackwell, vol. 30(1), pages 196-227, January.
    5. Aase, Knut K., 2005. "Using Option Pricing Theory to Infer About Equity Premiums," Discussion Papers 2005/11, Norwegian School of Economics, Department of Business and Management Science.

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    More about this item

    Keywords

    Optimal exercise policy; American put option; perpetual option; optimal stopping; incomplete markets; equity premiums; CCAPM.;
    All these keywords.

    JEL classification:

    • G00 - Financial Economics - - General - - - General

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