“ Filtering and Calibrating a Self-Exciting Jump Diffusion Model for Oil Price by a Particle Markov Chain Monte Carlo Method ”

In this paper we propose a self-exciting jump diffusion model for oil price dynamics based on a Hawkes-type process. In particular, the jump intensity is stochastic and path dependent; so a jump will increase the probability of observing a new jump and this feature of the model aims at explaining the jumps clustering effect. Our model is very similar to that proposed by Hainaut & Moraux (2017) for equity market, although we assume the jump size normally distributed. Moreover, our filtering and calibration method relies on a different procedure. Indeed, we filter the latent jump intensity and estimate the model parameters according to a Particle Markov Chain Monte Carlo method proposed by Andrieu, Doucet & Holenstein (2010), which is well suited for nonlinear non-Gaussian dynamical models. Finally, we provide numerical simulations in order to test our approach. Joint work with Carlo Sgarra.