Pricing VIX Options Based on Mean-Reverting Models Driven by Information

Financial time series are dynamic and influenced by different types of information from the market. In this study, we propose new models for SPX and VIX options using the Hawkes process, jump process with stochastic intensity, and tempered stable process to capture these changes in financial time series based on three distinct characteristics of market information. We calculate the VIX option pricing formula using these models and find that the simplified VIX model based on VIX characteristics has significantly less pricing error than the consistent VIX model derived from the SPX model. Additionally, we show that the tempered stable process is better suited to describing the volatility, sparse large jumps, and infinite small jumps of VIX than other processes, resulting in improved pricing accuracy. Finally, we demonstrate that the infinitesimal jump in the tempered stable process can replace Brownian motion in the stochastic model, meaning that the latter has little value in improving pricing accuracy. This research contributes to the theory of SPX and VIX options and offers guidance for the development of other information-driven economic models