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Sensitivity Study of Heston Stochastic Volatility Model Using GPGPU

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Large-Scale Scientific Computing (LSSC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7116))

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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.

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References

  1. Andersen, L.B.G.: Efficient Simulation of the Heston Stochastic Volatility Model. Banc of America Securities, http://ssrn.com/abstract=946405

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  4. Black, F., Scholes, M.S.: The pricing of options and corporate liabilities. Journal of Political Economy 81(3), 637–654 (1973)

    Article  Google Scholar 

  5. Caflisch, R.: Monte Carlo and quasi-Monte Carlo methods. Acta Numerica 7, 1–49 (1998)

    Article  MathSciNet  Google Scholar 

  6. Gatheral, J.: The Volatility Surface: A Practitioner’s Guide. Wiley Finance (2006)

    Google Scholar 

  7. Glasserman, P.: Monte Carlo Methods in Financial Engineering. Springer, New York (2003)

    Google Scholar 

  8. Heston, S.: A closed-form solution for options with stochastic volatility. Review of Financial Studies 6, 327–343 (1993)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  10. Niederreiter, H.: Random Number Generations and Quasi-Monte Carlo Methods. SIAM, Philadelphia (1992)

    Book  Google Scholar 

  11. Owen, A.B.: Scrambling Sobo’l and Niederreiter-Xing points. Journal of Complexity 14, 466–489 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  13. CUDA, http://developer.nvidia.com/category/zone/cuda-zone

  14. SIMLAB, http://simlab.jrc.ec.europa.eu/

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Atanassov, E.I., Ivanovska, S. (2012). Sensitivity Study of Heston Stochastic Volatility Model Using GPGPU. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2011. Lecture Notes in Computer Science, vol 7116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29843-1_49

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  • DOI: https://doi.org/10.1007/978-3-642-29843-1_49

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29842-4

  • Online ISBN: 978-3-642-29843-1

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