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The perpetual American put option for jump-diffusions: Implications for equity premiums

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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. The probability distribution under the risk adjusted measure turns out to depend on the equity premium, which is not the case for the standard, continuous version. This difference is utilized to find intertemporal, equilibrium equity premiums. We apply this technique to the US equity data of the last century, and find an indication that the risk premium on equity was about two and a half per cent if the risk free short rate was around one per cent. On the other hand, if the latter rate was about four per cent, we similarly find that this corresponds to an equity premium of around four and a half per cent. The advantage with our approach is that we need only equity data and option pricing theory, no consumption data was necessary to arrive at these conclusions. 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., 2004. "The perpetual American put option for jump-diffusions: Implications for equity premiums," Discussion Papers 2004/19, Norwegian School of Economics, Department of Business and Management Science.
  • Handle: RePEc:hhs:nhhfms:2004_019
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    File URL: http://hdl.handle.net/11250/163726
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    References listed on IDEAS

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    5. Rietz, Thomas A., 1988. "The equity risk premium a solution," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 117-131, July.
    6. Jan Ubøe & Bernt Øksendal & Knut Aase & Nicolas Privault, 2000. "White noise generalizations of the Clark-Haussmann-Ocone theorem with application to mathematical finance," Finance and Stochastics, Springer, vol. 4(4), pages 465-496.
    7. 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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    12. Knut Aase, 1999. "An Equilibrium Model of Catastrophe Insurance Futures and Spreads," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 24(1), pages 69-96, June.
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    14. Aase, Knut K., 2004. "Jump Dynamics: The Equity Premium and the Risk-Free Rate Puzzles," Discussion Papers 2004/12, 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;

    JEL classification:

    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets

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