A Comparison of Biased Simulation Schemes for Stochastic Volatility Models
Roger Lord (),
Remmert Koekkoek () and
Dick van Dijk ()
Additional contact information
Roger Lord: Erasmus Universiteit Rotterdam, and Rabobank
Remmert Koekkoek: Robeco Alternative Investments
No 06-046/4, Tinbergen Institute Discussion Papers from Tinbergen Institute
This discussion paper resulted in a publication in 'Quantitative Finance' , 2010, 10, 177-194. When using an Euler discretisation to simulate a mean-reverting square root process, one runs into 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 Heston stochastic volatility model, where the variance is modelled as a square root 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 upward bias found when pricing European options. Thirdly and finally, we numerically compare all Euler fixes to a recent quasi-second order scheme of Kahl and Jäckel and the exact scheme of Broadie and Kaya. The choice of fix is found to be extremely important. The full truncation scheme by far outperforms all biased schemes in terms of bias, root-mean-squared error, and hence should be the preferred discretisation method for simulation of the Heston model and extensions thereof.
Keywords: Stochastic volatility; Heston; square root process; Euler-Maruyama; discretisation; strong convergence; weak convergence; boundary behaviour (search for similar items in EconPapers)
JEL-codes: C63 G13 (search for similar items in EconPapers)
Date: 2006-05-18, Revised 2007-06-07
References: View references in EconPapers View complete reference list from CitEc
Citations Track citations by RSS feed
Downloads: (external link)
Journal Article: A comparison of biased simulation schemes for stochastic volatility models (2010)
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:tin:wpaper:20060046
Access Statistics for this paper
More papers in Tinbergen Institute Discussion Papers from Tinbergen Institute Contact information at EDIRC.
Series data maintained by Tinbergen Office +31 (0)10-4088900 ().