IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1504.02896.html
   My bibliography  Save this paper

Pricing and Risk Management with High-Dimensional Quasi Monte Carlo and Global Sensitivity Analysis

Author

Listed:
  • Marco Bianchetti
  • Sergei Kucherenko
  • Stefano Scoleri

Abstract

We review and apply Quasi Monte Carlo (QMC) and Global Sensitivity Analysis (GSA) techniques to pricing and risk management (greeks) of representative financial instruments of increasing complexity. We compare QMC vs standard Monte Carlo (MC) results in great detail, using high-dimensional Sobol' low discrepancy sequences, different discretization methods, and specific analyses of convergence, performance, speed up, stability, and error optimization for finite differences greeks. We find that our QMC outperforms MC in most cases, including the highest-dimensional simulations and greeks calculations, showing faster and more stable convergence to exact or almost exact results. Using GSA, we are able to fully explain our findings in terms of reduced effective dimension of our QMC simulation, allowed in most cases, but not always, by Brownian bridge discretization. We conclude that, beyond pricing, QMC is a very promising technique also for computing risk figures, greeks in particular, as it allows to reduce the computational effort of high-dimensional Monte Carlo simulations typical of modern risk management.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:1504.02896
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1504.02896
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Liu, Ruixue & Owen, Art B., 2006. "Estimating Mean Dimensionality of Analysis of Variance Decompositions," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 712-721, June.
    2. Kucherenko, Sergei & Feil, Balazs & Shah, Nilay & Mauntz, Wolfgang, 2011. "The identification of model effective dimensions using global sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 96(4), pages 440-449.
    3. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May.
    4. Peter L. Bossaerts & Bernt Arne Ødegaard, 2001. "Finance," World Scientific Book Chapters, in: Lectures On Corporate Finance, chapter 1, pages 3-5, World Scientific Publishing Co. Pte. Ltd..
    5. Xiaoqun Wang, 2009. "Dimension Reduction Techniques in Quasi-Monte Carlo Methods for Option Pricing," INFORMS Journal on Computing, INFORMS, vol. 21(3), pages 488-504, August.
    6. Spassimir H. Paskov & Joseph F. Traub, 1995. "Faster Valuation of Financial Derivatives," Working Papers 95-03-034, Santa Fe Institute.
    7. Sobol Ilya M. & Shukhman Boris V., 2014. "Quasi-Monte Carlo: A high-dimensional experiment," Monte Carlo Methods and Applications, De Gruyter, vol. 20(3), pages 167-171, September.
    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. Andrea Maran & Andrea Pallavicini & Stefano Scoleri, 2021. "Chebyshev Greeks: Smoothing Gamma without Bias," Papers 2106.12431, arXiv.org.
    2. Jan Posp'iv{s}il & Tom'av{s} Sobotka & Philipp Ziegler, 2019. "Robustness and sensitivity analyses for stochastic volatility models under uncertain data structure," Papers 1912.06709, arXiv.org.
    3. Julien Hok & Sergei Kucherenko, 2021. "Pricing and Risk Analysis in Hyperbolic Local Volatility Model with Quasi Monte Carlo," Papers 2106.08421, arXiv.org.
    4. Jan Pospíšil & Tomáš Sobotka & Philipp Ziegler, 2019. "Robustness and sensitivity analyses for stochastic volatility models under uncertain data structure," Empirical Economics, Springer, vol. 57(6), pages 1935-1958, December.
    5. Paul Bilokon & Sergei Kucherenko & Casey Williams, 2022. "Quasi-Monte Carlo methods for calculating derivatives sensitivities on the GPU," Papers 2209.11337, arXiv.org.
    6. J. Hok & S. Kucherenko, 2022. "The importance of being scrambled: supercharged Quasi Monte Carlo," Papers 2210.16548, arXiv.org, revised Oct 2023.
    7. Zhijian He & Xiaoqun Wang, 2021. "An Integrated Quasi-Monte Carlo Method for Handling High Dimensional Problems with Discontinuities in Financial Engineering," Computational Economics, Springer;Society for Computational Economics, vol. 57(2), pages 693-718, February.

    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. Xiaoqun Wang, 2016. "Handling Discontinuities in Financial Engineering: Good Path Simulation and Smoothing," Operations Research, INFORMS, vol. 64(2), pages 297-314, April.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Xiaoqun Wang & Ian H. Sloan, 2011. "Quasi-Monte Carlo Methods in Financial Engineering: An Equivalence Principle and Dimension Reduction," Operations Research, INFORMS, vol. 59(1), pages 80-95, February.
    7. Nicola Cufaro Petroni & Piergiacomo Sabino, 2013. "Pricing and Hedging Asian Basket Options with Quasi-Monte Carlo Simulations," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 147-163, March.
    8. Ingo Beyna, 2013. "Interest Rate Derivatives," Lecture Notes in Economics and Mathematical Systems, Springer, edition 127, number 978-3-642-34925-6, December.
    9. Sobol Ilya M. & Shukhman Boris V., 2014. "Quasi-Monte Carlo: A high-dimensional experiment," Monte Carlo Methods and Applications, De Gruyter, vol. 20(3), pages 167-171, September.
    10. Xiaoqun Wang, 2009. "Dimension Reduction Techniques in Quasi-Monte Carlo Methods for Option Pricing," INFORMS Journal on Computing, INFORMS, vol. 21(3), pages 488-504, August.
    11. Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June.
    12. 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.
    13. F. Y. Kuo & W. T. M. Dunsmuir & I. H. Sloan & M. P. Wand & R. S. Womersley, 2008. "Quasi-Monte Carlo for Highly Structured Generalised Response Models," Methodology and Computing in Applied Probability, Springer, vol. 10(2), pages 239-275, June.
    14. Riccardo Rebonato & Ian Cooper, 1998. "Coupling backward induction with Monte Carlo simulations: a fast Fourier transform (FFT) approach," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(2), pages 131-141.
    15. Josh Lerner, 2002. "Where Does State Street Lead? A First Look at Finance Patents, 1971 to 2000," Journal of Finance, American Finance Association, vol. 57(2), pages 901-930, April.
    16. Kucherenko, Sergei & Song, Shufang & Wang, Lu, 2019. "Quantile based global sensitivity measures," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 35-48.
    17. 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.
    18. Collan, Mikael, 2008. "New Method for Real Option Valuation Using Fuzzy Numbers," Working Papers 466, IAMSR, Åbo Akademi.
    19. Stentoft, Lars, 2005. "Pricing American options when the underlying asset follows GARCH processes," Journal of Empirical Finance, Elsevier, vol. 12(4), pages 576-611, September.
    20. 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.

    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:1504.02896. 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.