TY - JOUR
T1 - A regime-switching Heston model for VIX and S&P 500 implied volatilities
AU - Papanicolaou, Andrew
AU - Sircar, Ronnie
N1 - Funding Information:
The authors thank Lisa Goldberg for discussion on regime models, as well as Jim Gatheral and two anonymous referees for their helpful comments. Work by A.P. partially supported by NSF grant DMS-0739195, and R.S. partially supported by NSF grant DMS-1211906.
Publisher Copyright:
© 2014, Taylor & Francis Group, LLC.
PY - 2014/10/1
Y1 - 2014/10/1
N2 - Volatility products have become popular in the past 15 years as a hedge against market uncertainty. In particular, there is growing interest in options on the VIX volatility index. A number of recent empirical studies have examine whether there is significantly greater risk premium in VIX option prices compared with S&P 500 option prices. We address this issue by proposing and analysing a stochastic volatility model with regime switching. The basic Heston model cannot capture VIX-implied volatilities, as has been documented. We show that the incorporation of sharp regime shifts can bridge this shortcoming. We take advantage of asymptotic and Fourier methods to make the extension tractable, and we present a fit to data, both in times of crisis and relative calm, which shows the effectiveness of the regime switching.
AB - Volatility products have become popular in the past 15 years as a hedge against market uncertainty. In particular, there is growing interest in options on the VIX volatility index. A number of recent empirical studies have examine whether there is significantly greater risk premium in VIX option prices compared with S&P 500 option prices. We address this issue by proposing and analysing a stochastic volatility model with regime switching. The basic Heston model cannot capture VIX-implied volatilities, as has been documented. We show that the incorporation of sharp regime shifts can bridge this shortcoming. We take advantage of asymptotic and Fourier methods to make the extension tractable, and we present a fit to data, both in times of crisis and relative calm, which shows the effectiveness of the regime switching.
KW - Applied mathematical finance
KW - Calibration of stochastic volatility
KW - Model calibration
KW - VIX options
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U2 - 10.1080/14697688.2013.814923
DO - 10.1080/14697688.2013.814923
M3 - Article
AN - SCOPUS:84926198079
SN - 1469-7688
VL - 14
SP - 1811
EP - 1827
JO - Quantitative Finance
JF - Quantitative Finance
IS - 10
ER -