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Truncation and acceleration of the Tian tree for the pricing of American put options

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  • Ting Chen
  • Mark Joshi

Abstract

We present a new method for truncating binomial trees based on using a tolerance to control truncation errors and apply it to the Tian tree together with acceleration techniques of smoothing and Richardson extrapolation. For both the current (based on standard deviations) and the new (based on tolerance) truncation methods, we test different truncation criteria, levels and replacement values to obtain the best combination for each required level of accuracy. We also provide numerical results demonstrating that the new method can be 50% faster than previously presented methods when pricing American put options in the Black--Scholes model.

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  • Ting Chen & Mark Joshi, 2012. "Truncation and acceleration of the Tian tree for the pricing of American put options," Quantitative Finance, Taylor & Francis Journals, vol. 12(11), pages 1695-1708, November.
    • Handle: RePEc:taf:quantf:v:12:y:2012:i:11:p:1695-1708
    DOI: 10.1080/14697688.2011.617776
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    References listed on IDEAS

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    1. Leisen, Dietmar P. J., 1998. "Pricing the American put option: A detailed convergence analysis for binomial models," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1419-1444, August.
    2. Jiun Hong Chan & Mark Joshi & Robert Tang & Chao Yang, 2009. "Trinomial or binomial: Accelerating American put option price on trees," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 29(9), pages 826-839, September.
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    7. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-1250.
    8. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    9. Ju, Nengjiu, 1998. "Pricing an American Option by Approximating Its Early Exercise Boundary as a Multipiece Exponential Function," Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 627-646.
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    Cited by:

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