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A comparison of biased simulation schemes for stochastic volatility models

[journal article]

Lord, Roger; Koekkoek, Remmert; Dijk, Dick van

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Abstract Using an Euler discretisation to simulate a mean-reverting CEV process gives rise to 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 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 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 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 Jäckel 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.
Classification Basic Research, General Concepts and History of Economics; Economic Statistics, Econometrics, Business Informatics
Method theory application
Free Keywords Stochastic volatility; Heston; Square root process; CEV process; Euler-Maruyama; Discretization; Strong convergence; Weak convergence; Boundary behaviour
Document language English
Publication Year 2010
Page/Pages p. 177-194
Journal Quantitative Finance, 10 (2010) 2
Status Postprint; reviewed
Licence PEER Licence Agreement (applicable only to documents from PEER project)