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Using Richardson extrapolation techniques to price American options with alternative stochastic processes

Author

Listed:
  • Chuang-Chang Chang
  • Jun-Biao Lin
  • Wei-Che Tsai
  • Yaw-Huei Wang

Abstract

In this paper the authors investigate the performance of the original and repeated Richardson extrapolation methods for American option pricing by implementing both the original and modified Geske–Johnson approximation formulae. A comprehensive numerical comparison includes alternative stochastic processes of the underlying asset price. The numerical results show that whether the original or modified formula is implemented, the Richardson extrapolation techniques work very well. The repeated Richardson extrapolation strongly outperforms the original, especially when the underlying asset price follows a stochastic volatility process. Moreover, this study verifies the feasibility of the estimated error bounds of the American option prices under alternative stochastic processes by applying the repeated Richardson extrapolation method and estimating the interval of true American option values, as well as determining the number of options needed for an approximation to achieve a desired accuracy level. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Chuang-Chang Chang & Jun-Biao Lin & Wei-Che Tsai & Yaw-Huei Wang, 2012. "Using Richardson extrapolation techniques to price American options with alternative stochastic processes," Review of Quantitative Finance and Accounting, Springer, vol. 39(3), pages 383-406, October.
    • Handle: RePEc:kap:rqfnac:v:39:y:2012:i:3:p:383-406
    DOI: 10.1007/s11156-011-0253-0
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    Cited by:

    1. Jitka Hilliard & Wei Li, 2014. "Volatilities implied by price changes in the S&P 500 options and futures contracts," Review of Quantitative Finance and Accounting, Springer, vol. 42(4), pages 599-626, May.
    2. Jamal Amani Rad & Kourosh Parand & Saeid Abbasbandy, 2014. "Local weak form meshless techniques based on the radial point interpolation (RPI) method and local boundary integral equation (LBIE) method to evaluate European and American options," Papers 1412.6063, arXiv.org.
    3. Panayiotis Andreou & Chris Charalambous & Spiros Martzoukos, 2014. "Assessing the performance of symmetric and asymmetric implied volatility functions," Review of Quantitative Finance and Accounting, Springer, vol. 42(3), pages 373-397, April.

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    More about this item

    Keywords

    American options; Richardson extrapolation; Repeated Richardson extrapolation; Stochastic process; G13;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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