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The Sensitivity of American Options to Suboptimal Exercise Strategies

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  • Ibáñez, Alfredo
  • Paraskevopoulos, Ioannis

Abstract

The value of American options depends on the exercise policy followed by option holders. Market frictions, risk aversion, or a misspecified model, for example, can result in suboptimal behavior. We study the sensitivity of American options to suboptimal exercise strategies. We show that this measure is given by the Gamma of the American option at the optimal exercise boundary. More precisely, “if B is the optimal exercise price, but exercise is either brought forward when or delayed until a price B̃ has been reached, the cost of suboptimal exercise is given by ½ × Γ(B) × (B − B̃)2, where Γ(B) denotes the American option Gamma.” Therefore, the cost of suboptimal exercise is second-order in the bias of the exercise policy and depends on Gamma. This result provides new insights on American options.

Suggested Citation

  • Ibáñez, Alfredo & Paraskevopoulos, Ioannis, 2010. "The Sensitivity of American Options to Suboptimal Exercise Strategies," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(6), pages 1563-1590, December.
    • Handle: RePEc:cup:jfinqa:v:45:y:2011:i:06:p:1563-1590_00
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    Cited by:

    1. Cosma, Antonio & Galluccio, Stefano & Scaillet, Olivier, 2012. "Valuing American options using fast recursive projections," Working Papers unige:41856, University of Geneva, Geneva School of Economics and Management.
    2. Fabozzi, Frank J. & Paletta, Tommaso & Stanescu, Silvia & Tunaru, Radu, 2016. "An improved method for pricing and hedging long dated American options," European Journal of Operational Research, Elsevier, vol. 254(2), pages 656-666.
    3. Jorge Cruz Lopez & Alfredo Ibanez, 2020. "European Puts, Credit Protection, and Endogenous Default," University of Western Ontario, Departmental Research Report Series 20205, University of Western Ontario, Department of Economics.
    4. Chockalingam, Arun & Feng, Haolin, 2015. "The implication of missing the optimal-exercise time of an American option," European Journal of Operational Research, Elsevier, vol. 243(3), pages 883-896.
    5. Anna Kamille Nyegaard & Johan Raunkjær Ott & Mogens Steffensen, 2021. "An Intrinsic Value Approach to Valuation with Forward–Backward Loops in Dividend Paying Stocks," Mathematics, MDPI, vol. 9(13), pages 1-23, June.
    6. Sha Lin & Song‐Ping Zhu, 2022. "Pricing callable–puttable convertible bonds with an integral equation approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(10), pages 1856-1911, October.
    7. Fabozzi, Frank J. & Paletta, Tommaso & Tunaru, Radu, 2017. "An improved least squares Monte Carlo valuation method based on heteroscedasticity," European Journal of Operational Research, Elsevier, vol. 263(2), pages 698-706.

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