Advertisement

Sensitivity Study of Heston Stochastic Volatility Model Using GPGPU

  • Emanouil I. Atanassov
  • Sofiya Ivanovska
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7116)

Abstract

The focus of this paper is on effective parallel implementation of Heston Stochastic Volatility Model using GPGPU. This model is one of the most widely used stochastic volatility (SV) models. The method of Andersen provides efficient simulation of the stock price and variance under the Heston model. In our implementation of this method we tested the usage of both pseudo-random and quasi-random sequences in order to evaluate the performance and accuracy of the method.

We used it for computing Sobol’ sensitivity indices of the model with respect to input parameters. Since this method is computationally intensive, we implemented a parallel GPGPU-based version of the algorithm, which decreases substantially the computational time. In this paper we describe in detail our implementation and discuss numerical and timing results.

Keywords

Option Price Sensitivity Index Stochastic Volatility Implied Volatility Stochastic Volatility Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Andersen, L.B.G.: Efficient Simulation of the Heston Stochastic Volatility Model. Banc of America Securities, http://ssrn.com/abstract=946405
  2. 2.
    Atanassov, E.: A New Efficient Algorithm for Generating the Scrambled Sobol’ Sequence. In: Dimov, I.T., Lirkov, I., Margenov, S., Zlatev, Z. (eds.) NMA 2002. LNCS, vol. 2542, pp. 83–90. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  3. 3.
    Atanassov, E., Karaivanova, A., Ivanovska, S.: Tuning the Generation of Sobol Sequence with Owen Scrambling. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds.) LSSC 2009. LNCS, vol. 5910, pp. 459–466. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  4. 4.
    Black, F., Scholes, M.S.: The pricing of options and corporate liabilities. Journal of Political Economy 81(3), 637–654 (1973)CrossRefGoogle Scholar
  5. 5.
    Caflisch, R.: Monte Carlo and quasi-Monte Carlo methods. Acta Numerica 7, 1–49 (1998)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Gatheral, J.: The Volatility Surface: A Practitioner’s Guide. Wiley Finance (2006)Google Scholar
  7. 7.
    Glasserman, P.: Monte Carlo Methods in Financial Engineering. Springer, New York (2003)Google Scholar
  8. 8.
    Heston, S.: A closed-form solution for options with stochastic volatility. Review of Financial Studies 6, 327–343 (1993)CrossRefGoogle Scholar
  9. 9.
    Christoffersen, P., Heston, S.L., Jacobs, K.: The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work so Well. Management Science - Management 55(12), 1914–1932 (2009)zbMATHCrossRefGoogle Scholar
  10. 10.
    Niederreiter, H.: Random Number Generations and Quasi-Monte Carlo Methods. SIAM, Philadelphia (1992)CrossRefGoogle Scholar
  11. 11.
    Owen, A.B.: Scrambling Sobo’l and Niederreiter-Xing points. Journal of Complexity 14, 466–489 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Sobol, I.M.: Global Sensitivity Indices for Nonlinear Mathematical Models and Their Monte Carlo Estimates. Mathematics and Computers in Simulation 55(1-3), 271–280 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
  14. 14.

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Emanouil I. Atanassov
    • 1
  • Sofiya Ivanovska
    • 1
  1. 1.Institute of Information and Communication TechnlogiesBulgarian Academy of SciencesSofiaBulgaria

Personalised recommendations