Consistent pricing of VIX options with the Hawkes jump-diffusion model

This paper presents a valuation of VIX options employing a Hawkes jump-diffusion model that captures the clustering pattern of jumps observed extensively in the financial markets. In the consistent framework, the valuation problem of VIX options is solved efficiently via the Fourier cosine expansion (COS) method. The Monte Carlo (MC) simulations are carried out to demonstrate the reliability and efficiency of the COS method. Furthermore, a sensitivity analysis is performed to show how option prices response to different parameters associated with jump clustering. Finally, empirical studies are conducted to provide evidence to support our jump specification in matching the VIX option surface.