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Fast Ninomiya-Victoir Calibration of the Double-Mean-Reverting Model

Quantitative Finance, Vol. 13, No. 11, pp.1813-1829, 2013

38 Pages Posted: 2 Feb 2013 Last revised: 13 Jan 2014

Christian Bayer

Weierstras Institute for Applied Analysis and Stochastics (WIAS)

Jim Gatheral

CUNY Baruch College

Morten Karlsmark

University of Copenhagen - Department of Mathematical Sciences

Date Written: February 1, 2013

Abstract

We consider the three factor double mean reverting (DMR) model of Gatheral (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 (2008) and compare these to the Euler-Maruyama scheme with full truncation of Lord et al. (2010), 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.

Keywords: Stochastic volatility, double mean reverting, Cubature, second order Monte Carlo schemes

JEL Classification: G12, G13, C63

Suggested Citation

Bayer, Christian and Gatheral, Jim and Karlsmark, Morten, Fast Ninomiya-Victoir Calibration of the Double-Mean-Reverting Model (February 1, 2013). Quantitative Finance, Vol. 13, No. 11, pp.1813-1829, 2013. Available at SSRN: https://ssrn.com/abstract=2210420 or http://dx.doi.org/10.2139/ssrn.2210420

Christian Bayer

Weierstras Institute for Applied Analysis and Stochastics (WIAS) ( email )

Mohrenstr. 39
Berlin, 10117
Germany

Jim Gatheral (Contact Author)

CUNY Baruch College ( email )

Department of Mathematics
One Bernard Baruch Way
New York, NY 10010
United States

Morten Karlsmark

University of Copenhagen - Department of Mathematical Sciences ( email )

Universitetsparken 5
Copenhagen Ø, DK-2100
Denmark

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