Flexibly Modelling Volatility and Jumps Using Realised and Bi-Power Variation

Abstract

The importance of including jumps in prices in models of financial returns has long been understood. However, there has been relatively little work considering the dynamics of the jumps. In this paper, a stochastic volatility model with jumps is developed in which the jumps follow a Hawkes process which depends on the volatility process. Inference is made using returns, realised variation and bi-power variation (to provide information about the volatility process and jump process) and an emphasis is placed on flexible Bayesian methods. The method is applied to data from three stock indices: the S & P 500 index, the FTSE 100 index and Nikkei 225 index. The results illustrate the important role that volatility plays in the dynamics of the jump process.

Keywords: Stochastic volatility, realised measures, Bayesian nonparametrics, Hawkes processes, jump processes