The Role of the Conditional Skewness and Kurtosis in VIX Index Valuation

Abstract

The CBOE VIX index is a widely recognised benchmark measure of expected stock market volatility. As shown in the literature, probability distributions other than Gaussian are key features required to describe the dynamics of the S&P 500, the variable that ultimately determines the VIX index level. As such, it is important to assess if deviations from the Gaussian distribution have important impacts on the VIX index level. We examine herein how a model articulated over a time‐varying non‐Gaussian distribution with conditional skewness and kurtosis can contribute to the overall explanation of the VIX dynamics.

Discriminating Between GARCH Models for Option Pricing by Their Ability to Compute Accurate VIX Measures

“…12 In this case, and only in this case, the methodology of Lalancette & Simonato (2017) will be used to approximate VIX performance measures using Monte-Carlo methods. 13 In the bulk of recent studies (Christoffersen et al (2012), Kanniainen et al…”

“…6 When closed-form expressions are not available, two recent studies proposed interesting alternatives. In Lalancette & Simonato (2017) the authors proposed, for the NGARCH model with Johnson S U distributed driving noise, numerical approximations to make possible the computation of the implied VIX index using Monte-Carlo simulations. In Chorro & Fanirisoa (2018) a new estimation strategy for some non-Gaussian GARCH models is presented to include options or VIX information in the joint estimation at a low computational cost.…”

“…To our knowledge, in the existing literature, empirical studies questioned, in general, the impact of the distribution (Christoffersen et al (2006a), Chorro et al (2012)), the choice of the SDF (Badescu et al (2011), Christoffersen et al (2013), Chorro & Fanirisoa (2019)) or the estimation strategy ( Hao & Zhang (2013), Kanniainen et al (2014), Papantonis (2016), Lalancette & Simonato (2017)) on pricing performances, but none of them consider all these factors at the same time. For example, in Christoffersen et al (2004) and Kanniainen et al (2014) the authors study different GARCH structures with different estimation strategies, but restrict themselves to the Gaussian setting while in Chorro & Fanirisoa (2019) the authors focus on different SDF and estimation strategies only for the IG-GARCH model.…”

“…under the quadratic SDF.Unfortunately, in the case of NIG innovations (a notable exception is the NIG NGARCH model associated with the EGP ofBadescu et al (2019)) or when an exponential-quadratic SDF is used with the Gaussian NGARCH and GJR structures we do not have closed-form formulas for the implied Vix t . However, as explained inLalancette & Simonato (2017) we can still use Monte-Carlo simulations to approximate conditional expectation E Q [h t+j | F t ] and Vix t .…”

Compound distributions for financial returns

“…For details about how skewness and kurtosis can be used to improve model fitting and forecasting performance, see Feunou et al [ 57 ] and Lalancette and Simonato [ 58 ].…”