VIX option pricing-Applied by affine models with tempered stable processes and stochastic parameter

Taking into account the characteristics of VIX time series, such as mean reverting, leptokurtosis, biased, asymmetric jump and volatility clustering, this paper establishes an affine tempered stable model based on stochastic volatility that is viewed from the perspective of calendar and intrinsic time. The characteristic function of VIX time series process, equivalent infinitesimal and probability method are simultaneously applied to obtain the simplest expression of option pricing. Through the application of these models and option pricing methods, it becomes possible to conduct parameter estimates and the pricing prediction of the VIX option pricing model. When compared with the general affine jump model, it is concluded that it better depicts the characteristics of the VIX time series, such as leptokurtosis, biased and asymmetric jump, and also enables better economic interpretation and feasibility. This study both enriches derivatives pricing theory, and also provides a number of references that enable investors to avoid risks and price derivatives. © 2020, Editorial Board of Journal of Systems Engineering Society of China. All right reserved.