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A comparison of biased simulation schemes for stochastic volatility models


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


Bitte beziehen Sie sich beim Zitieren dieses Dokumentes immer auf folgenden Persistent Identifier (PID):http://nbn-resolving.de/urn:nbn:de:0168-ssoar-221279

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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.
Klassifikation Allgemeines, spezielle Theorien und "Schulen", Methoden, Entwicklung und Geschichte der Wirtschaftswissenschaften; Wirtschaftsstatistik, Ökonometrie, Wirtschaftsinformatik
Methode Theorieanwendung
Freie Schlagwörter Stochastic volatility; Heston; Square root process; CEV process; Euler-Maruyama; Discretization; Strong convergence; Weak convergence; Boundary behaviour
Sprache Dokument Englisch
Publikationsjahr 2010
Seitenangabe S. 177-194
Zeitschriftentitel Quantitative Finance, 10 (2010) 2
DOI http://dx.doi.org/10.1080/14697680802392496
Status Postprint; begutachtet (peer reviewed)
Lizenz PEER Licence Agreement (applicable only to documents from PEER project)