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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Andersen, L.B.G.: Efficient Simulation of the Heston Stochastic Volatility Model. Banc of America Securities, http://ssrn.com/abstract=946405
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)
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)
Black, F., Scholes, M.S.: The pricing of options and corporate liabilities. Journal of Political Economy 81(3), 637–654 (1973)
Caflisch, R.: Monte Carlo and quasi-Monte Carlo methods. Acta Numerica 7, 1–49 (1998)
Gatheral, J.: The Volatility Surface: A Practitioner’s Guide. Wiley Finance (2006)
Glasserman, P.: Monte Carlo Methods in Financial Engineering. Springer, New York (2003)
Heston, S.: A closed-form solution for options with stochastic volatility. Review of Financial Studies 6, 327–343 (1993)
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)
Niederreiter, H.: Random Number Generations and Quasi-Monte Carlo Methods. SIAM, Philadelphia (1992)
Owen, A.B.: Scrambling Sobo’l and Niederreiter-Xing points. Journal of Complexity 14, 466–489 (1998)
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)
SIMLAB, http://simlab.jrc.ec.europa.eu/
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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
eBook Packages: Computer ScienceComputer Science (R0)