IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v13y2013i6p861-872.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/14697688.2012.762111
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/14697688.2012.762111?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. repec:dau:papers:123456789/11984 is not listed on IDEAS
    3. 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.
    4. Naoki Kishimoto, 2004. "Pricing Path-Dependent Securities by the Extended Tree Method," Management Science, INFORMS, vol. 50(9), pages 1235-1248, September.
    5. 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.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Dong, Wenfeng & Kang, Boda, 2019. "Analysis of a multiple year gas sales agreement with make-up, carry-forward and indexation," Energy Economics, Elsevier, vol. 79(C), pages 76-96.
    2. Zhiqiang Zhou & Wei Xu & Alexey Rubtsov, 2024. "Joint calibration of S&P 500 and VIX options under local stochastic volatility models," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 29(1), pages 273-310, January.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dong, Wenfeng & Kang, Boda, 2019. "Analysis of a multiple year gas sales agreement with make-up, carry-forward and indexation," Energy Economics, Elsevier, vol. 79(C), pages 76-96.
    2. Pringles, Rolando & Olsina, Fernando & Penizzotto, Franco, 2020. "Valuation of defer and relocation options in photovoltaic generation investments by a stochastic simulation-based method," Renewable Energy, Elsevier, vol. 151(C), pages 846-864.
    3. Song-Ping Zhu & Xin-Jiang He, 2018. "A hybrid computational approach for option pricing," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 1-16, September.
    4. Zineb El Filali Ech-Chafiq & Pierre Henry-Labordere & Jérôme Lelong, 2021. "Pricing Bermudan options using regression trees/random forests," Working Papers hal-03436046, HAL.
    5. Joseph Y. J. Chow & Amelia C. Regan, 2011. "Real Option Pricing of Network Design Investments," Transportation Science, INFORMS, vol. 45(1), pages 50-63, February.
    6. Seiji Harikae & James S. Dyer & Tianyang Wang, 2021. "Valuing Real Options in the Volatile Real World," Production and Operations Management, Production and Operations Management Society, vol. 30(1), pages 171-189, January.
    7. Andrea Gamba & Nicola Fusari, 2009. "Valuing Modularity as a Real Option," Management Science, INFORMS, vol. 55(11), pages 1877-1896, November.
    8. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    9. Doan, Viet_Dung & Gaikwad, Abhijeet & Bossy, Mireille & Baude, Françoise & Stokes-Rees, Ian, 2010. "Parallel pricing algorithms for multi-dimensional Bermudan/American options using Monte Carlo methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(3), pages 568-577.
    10. Haehl, Christian & Spinler, Stefan, 2018. "Capacity expansion under regulatory uncertainty:A real options-based study in international container shipping," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 113(C), pages 75-93.
    11. San-Lin Chung & Mark Shackleton, 2005. "On the use and improvement of Hull and White's control variate technique," Applied Financial Economics, Taylor & Francis Journals, vol. 15(16), pages 1171-1179.
    12. In oon Kim & Bong-Gyu Jang & Kyeong Tae Kim, 2013. "A simple iterative method for the valuation of American options," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 885-895, May.
    13. Duy Nguyen, 2018. "A hybrid Markov chain-tree valuation framework for stochastic volatility jump diffusion models," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(04), pages 1-30, December.
    14. Cosma, Antonio & Galluccio, Stefano & Pederzoli, Paola & Scaillet, Olivier, 2020. "Early Exercise Decision in American Options with Dividends, Stochastic Volatility, and Jumps," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(1), pages 331-356, February.
    15. Lars Stentoft, 2004. "Convergence of the Least Squares Monte Carlo Approach to American Option Valuation," Management Science, INFORMS, vol. 50(9), pages 1193-1203, September.
    16. Liu, Xiaoran & Ronn, Ehud I., 2020. "Using the binomial model for the valuation of real options in computing optimal subsidies for Chinese renewable energy investments," Energy Economics, Elsevier, vol. 87(C).
    17. Werner Hürlimann, 2012. "Valuation of fixed and variable rate mortgages: binomial tree versus analytical approximations," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 35(2), pages 171-202, November.
    18. Carmen Schiel & Simon Glöser-Chahoud & Frank Schultmann, 2019. "A real option application for emission control measures," Journal of Business Economics, Springer, vol. 89(3), pages 291-325, April.
    19. Li, Chenxu & Ye, Yongxin, 2019. "Pricing and Exercising American Options: an Asymptotic Expansion Approach," Journal of Economic Dynamics and Control, Elsevier, vol. 107(C), pages 1-1.
    20. Antonio Cosma & Stefano Galluccio & Paola Pederzoli & O. Scaillet, 2012. "Valuing American Options Using Fast Recursive Projections," Swiss Finance Institute Research Paper Series 12-26, Swiss Finance Institute.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:quantf:v:13:y:2013:i:6:p:861-872. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RQUF20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.