Advanced Search
MyIDEAS: Login to save this paper or follow this series

A Comparison of Biased Simulation Schemes for Stochastic Volatility Models

Contents:

Author Info

  • Roger Lord

    ()
    (Erasmus Universiteit Rotterdam, and Rabobank)

  • Remmert Koekkoek

    ()
    (Robeco Alternative Investments)

  • Dick van Dijk

    ()
    (Faculty of Economics, Erasmus Universiteit Rotterdam)

Abstract

When using an Euler discretisation to simulate a mean-reverting square root process, one runs into the problem that while the process itself is guaranteed to be nonnegative, the discretisation is not. Although an exact and efficient simulation algorithm exists for this process, at present this is not the case for the Heston stochastic volatility model, where the variance is modelled as a square root process. Consequently, when using an Euler discretisation, one must carefully think about how to fix negative variances. Our contribution is threefold. Firstly, we unify all Euler fixes into a single general framework. Secondly, we introduce the new full truncation scheme, tailored to minimise the upward bias found when pricing European options. Thirdly and finally, we numerically compare all Euler fixes to a recent quasi-second order scheme of Kahl and Jäckel and the exact scheme of Broadie and Kaya. The choice of fix is found to be extremely important. The full truncation scheme by far outperforms all biased schemes in terms of bias, root-mean-squared error, and hence should be the preferred discretisation method for simulation of the Heston model and extensions thereof.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://papers.tinbergen.nl/06046.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 06-046/4.

as in new window
Length:
Date of creation: 18 May 2006
Date of revision: 07 Jun 2007
Handle: RePEc:dgr:uvatin:20060046

Contact details of provider:
Web page: http://www.tinbergen.nl

Related research

Keywords: Stochastic volatility; Heston; square root process; Euler-Maruyama; discretisation; strong convergence; weak convergence; boundary behaviour;

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

No references listed on IDEAS
You can help add them by filling out this form.

Citations

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

Cited by:
  1. C. Kaebe & J. Maruhn & E. Sachs, 2009. "Adjoint-based Monte Carlo calibration of financial market models," Finance and Stochastics, Springer, vol. 13(3), pages 351-379, September.
  2. Eckhard Platen & Renata Rendek, 2009. "Exact Scenario Simulation for Selected Multi-dimensional Stochastic Processes," Research Paper Series 259, Quantitative Finance Research Centre, University of Technology, Sydney.
  3. Ewald, Christian-Oliver & Menkens, Olaf & Hung Marten Ting, Sai, 2013. "Asian and Australian options: A common perspective," Journal of Economic Dynamics and Control, Elsevier, vol. 37(5), pages 1001-1018.
  4. Roger Lord & Christian Kahl, 2006. "Why the Rotation Count Algorithm works," Tinbergen Institute Discussion Papers 06-065/2, Tinbergen Institute.
  5. Kilin, Fiodar, 2006. "Accelerating the calibration of stochastic volatility models," MPRA Paper 2975, University Library of Munich, Germany, revised 22 Apr 2007.
  6. Andreas Neuenkirch & Lukasz Szpruch, 2012. "First order strong approximations of scalar SDEs with values in a domain," Papers 1209.0390, arXiv.org.
  7. Rodrigue Oeuvray & Pascal Junod, 2013. "On time scaling of semivariance in a jump-diffusion process," Papers 1311.1122, arXiv.org.
  8. Carl Chiarella & Chih-Ying Hsiao & Thuy-Duong To, 2011. "Stochastic Correlation and Risk Premia in Term Structure Models," Research Paper Series 298, Quantitative Finance Research Centre, University of Technology, Sydney.
  9. Jessica Wachter, 2008. "Can time-varying risk of rare disasters explain aggregate stock market volatility?," 2008 Meeting Papers 944, Society for Economic Dynamics.
  10. F. Antonelli & A. Ramponi & S. Scarlatti, 2010. "Exchange option pricing under stochastic volatility: a correlation expansion," Review of Derivatives Research, Springer, vol. 13(1), pages 45-73, April.
  11. Xianming Sun & Siqing Gan, 2014. "An Efficient Semi-Analytical Simulation for the Heston Model," Computational Economics, Society for Computational Economics, vol. 43(4), pages 433-445, April.
  12. Dell'Era, Mario, 2010. "Geometrical Considerations on Heston's Market Model," MPRA Paper 21523, University Library of Munich, Germany.
  13. Paul Glasserman & Kyoung-Kuk Kim, 2011. "Gamma expansion of the Heston stochastic volatility model," Finance and Stochastics, Springer, vol. 15(2), pages 267-296, June.
  14. Dell'Era, Mario, 2010. "Geometrical Approximation method and stochastic volatility market models," MPRA Paper 22568, University Library of Munich, Germany.
  15. Dell'Era, Mario, 2010. "Vanilla Option Pricing on Stochastic Volatility market models," MPRA Paper 25645, University Library of Munich, Germany.
  16. Fahim, Arash & Touzi, Nizar & Warin, Xavier, 2011. "A Probabilistic Numerical Method for Fully Nonlinear Parabolic PDEs," Economics Papers from University Paris Dauphine 123456789/5524, Paris Dauphine University.
  17. repec:hal:wpaper:hal-00409861 is not listed on IDEAS
  18. Medvedev, Alexey & Scaillet, Olivier, 2010. "Pricing American options under stochastic volatility and stochastic interest rates," Journal of Financial Economics, Elsevier, vol. 98(1), pages 145-159, October.
  19. Campillo, Fabien & Joannides, Marc & Larramendy-Valverde, Irène, 2014. "Approximation of the Fokker–Planck equation of the stochastic chemostat," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 99(C), pages 37-53.
  20. Carl Chiarella & Susanne Griebsch & Boda Kang, 2013. "Investigating Time-Efficient Methods to Price Compound Options in the Heston Model," Research Paper Series 328, Quantitative Finance Research Centre, University of Technology, Sydney.
  21. Benjamin Jourdain & Mohamed Sbai, 2013. "High order discretization schemes for stochastic volatility models," Post-Print hal-00409861, HAL.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:dgr:uvatin:20060046. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Antoine Maartens (+31 626 - 160 892)).

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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