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Rationality parameter for exercising American put

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  • K. Gad
  • J. L. Pedersen

Abstract

The main result of this paper is a probabilistic proof of the penalty method for approximating the price of an American put in the Black-Scholes market. The method gives a parametrized family of partial differential equations, and by varying the parameter the corresponding solutions converge to the price of an American put. For each PDE the parameter may be interpreted as a rationality parameter of the holder of the option. The method may be extended to other valuation situations given as an optimal stopping problem with no explicit solution. The method may also be used for valuations where actors do not behave completely rationally but instead have randomness affecting their choices. The rationality parameter is a measure for this randomness.

Suggested Citation

  • K. Gad & J. L. Pedersen, 2014. "Rationality parameter for exercising American put," Papers 1410.1287, arXiv.org.
  • Handle: RePEc:arx:papers:1410.1287
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    References listed on IDEAS

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    1. Chen, Hsiao-Chi & Friedman, James W. & Thisse, Jacques-Francois, 1997. "Boundedly Rational Nash Equilibrium: A Probabilistic Choice Approach," Games and Economic Behavior, Elsevier, vol. 18(1), pages 32-54, January.
    2. Dai, Min & Kwok, Yue Kuen & You, Hong, 2007. "Intensity-based framework and penalty formulation of optimal stopping problems," Journal of Economic Dynamics and Control, Elsevier, vol. 31(12), pages 3860-3880, December.
    3. Allen M. Poteshman & Vitaly Serbin, 2003. "Clearly Irrational Financial Market Behavior: Evidence from the Early Exercise of Exchange Traded Stock Options," Journal of Finance, American Finance Association, vol. 58(1), pages 37-70, February.
    4. Diz, Fernando & Finucane, Thomas J, 1993. "The Rationality of Early Exercise Decisions: Evidence from the S&P 100 Index Options Market," Review of Financial Studies, Society for Financial Studies, vol. 6(4), pages 765-797.
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