Fast Ninomiya–Victoir calibration of the double-mean-reverting model

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  • Christian Bayer
  • Jim Gatheral
  • Morten Karlsmark
We consider the three-factor double mean reverting (DMR) option pricing model of Gatheral [Consistent Modelling of SPX and VIX Options, 2008], a model which can be successfully calibrated to both VIX options and SPX options simultaneously. One drawback of this model is that calibration may be slow because no closed form solution for European options exists. In this paper, we apply modified versions of the second-order Monte Carlo scheme of Ninomiya and Victoir [Appl. Math. Finance, 2008, 15, 107–121], and compare these to the Euler–Maruyama scheme with full truncation of Lord et al. [Quant. Finance, 2010, 10(2), 177–194], demonstrating on the one hand that fast calibration of the DMR model is practical, and on the other that suitably modified Ninomiya–Victoir schemes are applicable to the simulation of much more complicated time-homogeneous models than may have been thought previously.
Original languageEnglish
JournalQuantitative Finance
Volume13
Issue number11
Pages (from-to)1813-1826
ISSN1469-7688
DOIs
Publication statusPublished - 2013

ID: 115695060