Fast Ninomiya–Victoir calibration of the double-mean-reverting model
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Fast Ninomiya–Victoir calibration of the double-mean-reverting model. / Bayer, Christian ; Gatheral, Jim ; Karlsmark, Morten.
I: Quantitative Finance, Bind 13, Nr. 11, 2013, s. 1813-1826.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Fast Ninomiya–Victoir calibration of the double-mean-reverting model
AU - Bayer, Christian
AU - Gatheral, Jim
AU - Karlsmark, Morten
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
U2 - 10.1080/14697688.2013.818245
DO - 10.1080/14697688.2013.818245
M3 - Journal article
VL - 13
SP - 1813
EP - 1826
JO - Quantitative Finance
JF - Quantitative Finance
SN - 1469-7688
IS - 11
ER -
ID: 115695060