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A new sampling strategy willow tree method with application to path-dependent option pricing

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  • Wei Xu
  • Zhiwu Hong
  • Chenxiang Qin

Abstract

The willow tree algorithm, first developed by Curran in 1998, provides an efficient option pricing procedure. However, it leads to a large bias through Curran’s sampling strategy when the number of points at each time step is not large. Thus, in this paper, a new sampling strategy is proposed. Compared with Curran’s sampling strategy, the new strategy gives a much better estimation of the standard normal distribution with a small number of sampling points. We then apply the willow tree algorithm with the new sampling strategy to price path-dependent options such as American, Asian and American moving-average options. The numerical results illustrate that the willow tree algorithm is much more efficient than the least-squares Monte Carlo method and binomial tree method with higher precision.

Suggested Citation

  • Wei Xu & Zhiwu Hong & Chenxiang Qin, 2013. "A new sampling strategy willow tree method with application to path-dependent option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 861-872, May.
    • Handle: RePEc:taf:quantf:v:13:y:2013:i:6:p:861-872
    DOI: 10.1080/14697688.2012.762111
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    References listed on IDEAS

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    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    2. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    3. repec:dau:papers:123456789/11984 is not listed on IDEAS
    4. Dai, Min & Li, Peifan & Zhang, Jin E., 2010. "A lattice algorithm for pricing moving average barrier options," Journal of Economic Dynamics and Control, Elsevier, vol. 34(3), pages 542-554, March.
    5. Naoki Kishimoto, 2004. "Pricing Path-Dependent Securities by the Extended Tree Method," Management Science, INFORMS, vol. 50(9), pages 1235-1248, September.
    6. 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.
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    Cited by:

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    3. Ling Lu & Wei Xu & Zhehui Qian, 2017. "Efficient willow tree method for European-style and American-style moving average barrier options pricing," Quantitative Finance, Taylor & Francis Journals, vol. 17(6), pages 889-906, June.
    4. Xu, Wei & Šević, Aleksandar & Šević, Željko, 2022. "Implied volatility surface construction for commodity futures options traded in China," Research in International Business and Finance, Elsevier, vol. 61(C).
    5. Xu, Wei & Chen, Yuehuan & Coleman, Conrad & Coleman, Thomas F., 2018. "Moment matching machine learning methods for risk management of large variable annuity portfolios," Journal of Economic Dynamics and Control, Elsevier, vol. 87(C), pages 1-20.
    6. Dong, Bing & Xu, Wei & Sevic, Aleksandar & Sevic, Zeljko, 2020. "Efficient willow tree method for variable annuities valuation and risk management☆," International Review of Financial Analysis, Elsevier, vol. 68(C).
    7. Ludovic Gouden`ege & Andrea Molent & Antonino Zanette, 2021. "Moving average options: Machine Learning and Gauss-Hermite quadrature for a double non-Markovian problem," Papers 2108.11141, arXiv.org.
    8. Changfu Ma & Wei Xu & Yue Kuen Kwok, 2020. "Willow tree algorithms for pricing VIX derivatives under stochastic volatility models," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 1-28, March.
    9. Goudenège, Ludovic & Molent, Andrea & Zanette, Antonino, 2022. "Moving average options: Machine learning and Gauss-Hermite quadrature for a double non-Markovian problem," European Journal of Operational Research, Elsevier, vol. 303(2), pages 958-974.

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