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Rationality Parameter for Exercising American Put

Author

Listed:
  • 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, Open Access Journal, 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. 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. 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.
    3. 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.
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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.

    More about this item

    Keywords

    behavioral modeling; irrational exercise rule; partial differential equation; penalty method;

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • G0 - Financial Economics - - General
    • G1 - Financial Economics - - General Financial Markets
    • G2 - Financial Economics - - Financial Institutions and Services
    • G3 - Financial Economics - - Corporate Finance and Governance
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics
    • M4 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Accounting
    • K2 - Law and Economics - - Regulation and Business Law

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