A switching self-exciting jump diffusion process for stock prices.

Summary This study proposes a new Markov switching process with clustering eects. In this approach, a hidden Markov chain with a nite number of states modulates the parameters of a self-excited jump process combined to a geometric Brownian motion. Each regime corresponds to a particular economic cycle determining the expected return, the diusion coecient and the long-run frequency of clustered jumps. We study rst the theoretical properties of this process and we propose a sequential Monte-Carlo method to lter the hidden state variables. We next develop a Markov Chain Monte-Carlo procedure to t the model to the S&P 500. Finally, we analyse the impact of such a jump clustering on implied volatilities of European options.