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Analytical Upper Bounds for American Option Prices

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  • Chen, Ren-Raw
  • Yeh, Shih-Kuo

Abstract

American options require numerical methods, namely lattice models, to provide accurate price estimates. The computations can become expensive when more than one state variable is involved. Analytical upper bounds can therefore provide a useful guideline for how high American values can reach. In this paper, we derive analytical (closed-form) upper bounds for American option prices under stochastic interest rates, stochastic volatility, and jumps where American option prices are difficult to compute with accuracy. In a stochastic volatility model (Heston (1993) and Scott (1997)) that has two random factors, we demonstrate that the upper bound only takes a very small fraction of the time that the American option needs to compute.

Suggested Citation

  • Chen, Ren-Raw & Yeh, Shih-Kuo, 2002. "Analytical Upper Bounds for American Option Prices," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(1), pages 117-135, March.
    • Handle: RePEc:cup:jfinqa:v:37:y:2002:i:01:p:117-135_00
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    Cited by:

    1. Li, Minqiang, 2008. "Closed-Form Approximations for Spread Option Prices and Greeks," MPRA Paper 6994, University Library of Munich, Germany.
    2. Ye Du & Shan Xue & Yanchu Liu, 2019. "Robust upper bounds for American put options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(1), pages 3-14, January.
    3. Jilong Chen & Christian Ewald, 2017. "On the Performance of the Comonotonicity Approach for Pricing Asian Options in Some Benchmark Models from Equities and Commodities," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-32, March.
    4. Jun Cheng & Jin Zhang, 2012. "Analytical pricing of American options," Review of Derivatives Research, Springer, vol. 15(2), pages 157-192, July.
    5. Ren-Raw Chen & Shih-Kuo Yeh, 2012. "Analytical bounds for Treasury bond futures prices," Review of Quantitative Finance and Accounting, Springer, vol. 39(2), pages 209-239, August.
    6. Chung, San-Lin & Hung, Mao-Wei & Wang, Jr-Yan, 2010. "Tight bounds on American option prices," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 77-89, January.
    7. John Handley, 2005. "On the Upper Bound of a Call Option," Review of Derivatives Research, Springer, vol. 8(2), pages 85-95, August.

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