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Rationality Parameter for Exercising American Put

Author

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  • Kamille Sofie Tågholt Gad

    (Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark)

  • Jesper Lund Pedersen

    (Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark)

Abstract

In this paper, irrational exercise behavior of the buyer of an American put is characterized by a single parameter. We model irrational exercise rules as the first jump time of a point processes with stochastic intensity. By the rationality parameter, we parameterize a family of stochastic intensities that depends on the value of the put itself. We present a probabilistic proof that the value of the American put using the irrational exercise rule converges to the arbitrage-free price as the rationality parameter converges to infinity. Another application of this result is the penalty method for approximating the price of an American put.

Suggested Citation

  • Kamille Sofie Tågholt Gad & Jesper Lund Pedersen, 2015. "Rationality Parameter for Exercising American Put," Risks, MDPI, vol. 3(2), pages 1-9, May.
    • Handle: RePEc:gam:jrisks:v:3:y:2015:i:2:p:103-111:d:49867
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    References listed on IDEAS

    as
    1. Diz, Fernando & Finucane, Thomas J, 1993. "The Rationality of Early Exercise Decisions: Evidence from the S&P 100 Index Options Market," The Review of Financial Studies, Society for Financial Studies, vol. 6(4), pages 765-797.
    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. 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.
    4. 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.
    5. Peter Carr & Vadim Linetsky, 2000. "The Valuation of Executive Stock Options in an Intensity-Based Framework," Review of Finance, European Finance Association, vol. 4(3), pages 211-230.
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    Cited by:

    1. Rafael Company & Vera Egorova & Lucas J'odar & Fazlollah Soleymani, 2017. "Computing stable numerical solutions for multidimensional American option pricing problems: a semi-discretization approach," Papers 1701.08545, arXiv.org.
    2. Fazlollah Soleymani, 2019. "Efficient Semi-Discretization Techniques for Pricing European and American Basket Options," Computational Economics, Springer;Society for Computational Economics, vol. 53(4), pages 1487-1508, April.

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