A Multifactor Self-Exciting Jump Diffusion Approach for Modelling the Clustering of Jumps in Equity Returns

Abstract

This paper introduces a new jump diffusion process where the occurrence and the size of past jumps have an impact on both the instantaneous and the long term propensities of observing a jump instantaneously. Here, the intensity of jump arrival is a multifactor self-excited process whereas the jump size is a double exponential random variable. This specification capture many dynamic features of asset returns; it can for instance handle with the jump clustering effects explored by Ait-Sahalia et al. (2015). Moreover, it remains analytically tractable, as we can prove that these multifactor self-excited processes are similar to single factor processes whose kernel function is the sum of two exponential functions. We can derive various closed and semi-closed form expressions for the mean and the variance of the intensity as well as for the moment generating of log returns. We also find a class of changes of measure that preserves the dynamics of the process under the risk neutral measure. To motivate empirically the multifactor model, we calibrate the model by a peak over threshold approach and filter state variables by sequential Monte Carlo algorithm. We also investigate if self-excitation is induced by positive, negative or both jumps. So as to illustrate the applicability of our modeling for derivatives, we next evaluate European options and analyze the sensitivity of implied volatilities to parameters and factors.

Keywords: Hawkes process, self exciting process, clustering effects

JEL Classification: G10, G11.