VIX derivatives: Valuation models and empirical evidence

Pricing VIX options with volatility clustering

“…So far, the previous studies on the pricing of VIX derivatives are classified into two main categories based on different modeling ideas. The first one is to model the joint dynamics of the S&P 500 index (SPX) and its instantaneous variance (e.g., Baldeaux & Badran, ; Lin & Chang, ; Lo, Shih, Wang, & Yu, ; Zhang & Zhu, ). The VIX, as a measure of the implied 30‐day volatility of the SPX options, can be derived from the joint dynamics.…”

“…The VIX log‐returns exhibit a high kurtosis suggesting the presence of large movements. To capture these large movements in volatility, it is typical to add a jump component, which is characterized by the compound Poisson processes, to the diffusion model in a study of pricing volatility options (e.g., Kaeck & Alexander, ; Lo et al, ; Psychoyios, Dotsis, & Markellos, ; Sepp, ). Unfortunately, to our best knowledge, existing models for the valuation of VIX options fail to replicate the pattern that extreme price movements are empirically highly clustered.…”

Instantaneous squared VIX and VIX derivatives

“…Later on, Lin (), Lu and Zhu (), Dupoyet, Daigler and Chen (), and Zhu and Lian () examine more complicated models for VIX futures. Meanwhile, Sepp (, ), Albanese, Lo, and Mijatović (), Lin and Chang (), Li (), Chung, Tsai, Wang, and Weng (), Wang and Daigler (), Chen and Poon (), Lian and Zhu (), Papanicolaou and Sircar (), Branger, Kraftschik, and Volkert (), Song and Xiu (), Lin, Li, Luo, and Chern (), Romo (), Bardgett, Gourier, and Leippold (), and Lo, Shih, Wang, and Yu () investigate various specifications for pricing VIX options. For example, Branger et al () compare consistent and log VIX models by focusing on both the first and the second moments of the VIX risk‐neutral distribution in addition to pricing errors.…”