A comparison of biased simulation schemes for stochastic volatility models
AbstractUsing an Euler discretization to simulate a mean-reverting CEV process gives rise to the problem that while the process itself is guaranteed to be nonnegative, the discretization is not. Although an exact and efficient simulation algorithm exists for this process, at present this is not the case for the CEV-SV stochastic volatility model, with the Heston model as a special case, where the variance is modelled as a mean-reverting CEV process. Consequently, when using an Euler discretization, 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 minimize the positive bias found when pricing European options. Thirdly and finally, we numerically compare all Euler fixes to recent quasi-second order schemes of Kahl and Jackel, and Ninomiya and Victoir, as well as to the exact scheme of Broadie and Kaya. The choice of fix is found to be extremely important. The full truncation scheme outperforms all considered biased schemes in terms of bias and root-mean-squared error.
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Bibliographic InfoArticle provided by Taylor & Francis Journals in its journal Quantitative Finance.
Volume (Year): 10 (2010)
Issue (Month): 2 ()
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Other versions of this item:
- Roger Lord & Remmert Koekkoek & Dick van Dijk, 2006. "A Comparison of Biased Simulation Schemes for Stochastic Volatility Models," Tinbergen Institute Discussion Papers 06-046/4, Tinbergen Institute, revised 07 Jun 2007.
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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- Jessica Wachter, 2008.
"Can time-varying risk of rare disasters explain aggregate stock market volatility?,"
2008 Meeting Papers
944, Society for Economic Dynamics.
- Jessica A. Wachter, 2013. "Can Time-Varying Risk of Rare Disasters Explain Aggregate Stock Market Volatility?," Journal of Finance, American Finance Association, vol. 68(3), pages 987-1035, 06.
- Jessica Wachter, 2008. "Can Time-Varying Risk of Rare Disasters Explain Aggregate Stock Market Volatility?," NBER Working Papers 14386, National Bureau of Economic Research, Inc.
- 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.
- 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.
- repec:hal:wpaper:hal-00409861 is not listed on IDEAS
- 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.
- 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.
- Dell'Era, Mario, 2010. "Geometrical Considerations on Heston's Market Model," MPRA Paper 21523, University Library of Munich, Germany.
- Rodrigue Oeuvray & Pascal Junod, 2013. "On time scaling of semivariance in a jump-diffusion process," Papers 1311.1122, arXiv.org.
- Kilin, Fiodar, 2006. "Accelerating the calibration of stochastic volatility models," MPRA Paper 2975, University Library of Munich, Germany, revised 22 Apr 2007.
- Dell'Era, Mario, 2010. "Geometrical Approximation method and stochastic volatility market models," MPRA Paper 22568, University Library of Munich, Germany.
- 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.
- 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.
- 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.
- Benjamin Jourdain & Mohamed Sbai, 2013. "High order discretization schemes for stochastic volatility models," Post-Print hal-00409861, HAL.
- Dell'Era, Mario, 2010. "Vanilla Option Pricing on Stochastic Volatility market models," MPRA Paper 25645, University Library of Munich, Germany.
- Roger Lord & Christian Kahl, 2006. "Why the Rotation Count Algorithm works," Tinbergen Institute Discussion Papers 06-065/2, Tinbergen Institute.
- 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.
- 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.
- 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.
- 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.
- Andreas Neuenkirch & Lukasz Szpruch, 2012. "First order strong approximations of scalar SDEs with values in a domain," Papers 1209.0390, arXiv.org.
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