A regime-switching Heston model for VIX and S&P 500 implied volatilities

Andrew Papanicolaou, Ronnie Sircar
2013 Quantitative finance (Print)  
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 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 analyzing a stochastic volatility model with regime switching. The basic Heston model cannot capture VIX implied
more » ... 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.
doi:10.1080/14697688.2013.814923 fatcat:yofc3u4rlnc5ll5evoyhwlzuti