IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2209.11337.html
   My bibliography  Save this paper

Quasi-Monte Carlo methods for calculating derivatives sensitivities on the GPU

Author

Listed:
  • Paul Bilokon
  • Sergei Kucherenko
  • Casey Williams

Abstract

The calculation of option Greeks is vital for risk management. Traditional pathwise and finite-difference methods work poorly for higher-order Greeks and options with discontinuous payoff functions. The Quasi-Monte Carlo-based conditional pathwise method (QMC-CPW) for options Greeks allows the payoff function of options to be effectively smoothed, allowing for increased efficiency when calculating sensitivities. Also demonstrated in literature is the increased computational speed gained by applying GPUs to highly parallelisable finance problems such as calculating Greeks. We pair QMC-CPW with simulation on the GPU using the CUDA platform. We estimate the delta, vega and gamma Greeks of three exotic options: arithmetic Asian, binary Asian, and lookback. Not only are the benefits of QMC-CPW shown through variance reduction factors of up to $1.0 \times 10^{18}$, but the increased computational speed through usage of the GPU is shown as we achieve speedups over sequential CPU implementations of more than $200$x for our most accurate method.

Suggested Citation

  • Paul Bilokon & Sergei Kucherenko & Casey Williams, 2022. "Quasi-Monte Carlo methods for calculating derivatives sensitivities on the GPU," Papers 2209.11337, arXiv.org.
    • Handle: RePEc:arx:papers:2209.11337
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2209.11337
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
    2. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
    3. Marco Bianchetti & Sergei Kucherenko & Stefano Scoleri, 2015. "Pricing and Risk Management with High-Dimensional Quasi Monte Carlo and Global Sensitivity Analysis," Papers 1504.02896, arXiv.org.
    4. Ye Xiao & Xiaoqun Wang, 2019. "Enhancing Quasi-Monte Carlo Simulation by Minimizing Effective Dimension for Derivative Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 54(1), pages 343-366, June.
    5. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. John Board & Charles Sutcliffe & William T. Ziemba, 2003. "Applying Operations Research Techniques to Financial Markets," Interfaces, INFORMS, vol. 33(2), pages 12-24, April.
    3. Orozco-Garcia, Carolina & Schmeiser, Hato, 2015. "How sensitive is the pricing of lookback and interest rate guarantees when changing the modelling assumptions?," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 77-93.
    4. Grosen, Anders & Lochte Jorgensen, Peter, 2000. "Fair valuation of life insurance liabilities: The impact of interest rate guarantees, surrender options, and bonus policies," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 37-57, February.
    5. E. Nasakkala & J. Keppo, 2008. "Hydropower with Financial Information," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(5-6), pages 503-529.
    6. Galai, Dan & Raviv, Alon & Wiener, Zvi, 2007. "Liquidation triggers and the valuation of equity and debt," Journal of Banking & Finance, Elsevier, vol. 31(12), pages 3604-3620, December.
    7. Hanbyeol Jang & Sangkwon Kim & Junhee Han & Seongjin Lee & Jungyup Ban & Hyunsoo Han & Chaeyoung Lee & Darae Jeong & Junseok Kim, 2020. "Fast Monte Carlo Simulation for Pricing Equity-Linked Securities," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 865-882, December.
    8. Shuai Gao & Jun Zhao, 2016. "Pricing 50ETF in the Way of American Options Based on Least Squares Monte Carlo Simulation," Applied Finance and Accounting, Redfame publishing, vol. 2(2), pages 71-76, August.
    9. Aintablian, Sebouh & Khoury, Wissam El, 2017. "A simulation on the presence of competing bidders in mergers and acquisitions," Finance Research Letters, Elsevier, vol. 22(C), pages 233-243.
    10. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    11. Xiaoqun Wang & Ken Seng Tan, 2013. "Pricing and Hedging with Discontinuous Functions: Quasi-Monte Carlo Methods and Dimension Reduction," Management Science, INFORMS, vol. 59(2), pages 376-389, July.
    12. Darae Jeong & Minhyun Yoo & Changwoo Yoo & Junseok Kim, 2019. "A Hybrid Monte Carlo and Finite Difference Method for Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 111-124, January.
    13. Tak Kuen Siu & Robert J. Elliott, 2019. "Hedging Options In A Doubly Markov-Modulated Financial Market Via Stochastic Flows," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-41, December.
    14. Valeriy Ryabchenko & Sergey Sarykalin & Stan Uryasev, 2004. "Pricing European Options by Numerical Replication: Quadratic Programming with Constraints," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(3), pages 301-333, September.
    15. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
    16. Nelson Areal & Artur Rodrigues & Manuel Armada, 2008. "On improving the least squares Monte Carlo option valuation method," Review of Derivatives Research, Springer, vol. 11(1), pages 119-151, March.
    17. Jin, Xing & Li, Xun & Tan, Hwee Huat & Wu, Zhenyu, 2013. "A computationally efficient state-space partitioning approach to pricing high-dimensional American options via dimension reduction," European Journal of Operational Research, Elsevier, vol. 231(2), pages 362-370.
    18. Michael A. Kouritzin, 2016. "Explicit Heston Solutions and Stochastic Approximation for Path-dependent Option Pricing," Papers 1608.02028, arXiv.org, revised Apr 2018.
    19. Manuel Moreno & Javier Navas, 2003. "On the Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives," Review of Derivatives Research, Springer, vol. 6(2), pages 107-128, May.
    20. Vasile BRÄ‚TIAN, 2018. "Evaluation of Options using the Monte Carlo Method and the Entropy of Information," Expert Journal of Economics, Sprint Investify, vol. 6(2), pages 35-43.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2209.11337. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.