A switching self-exciting jump diffusion process for stock prices

Donatien Hainaut (1) , Franck Moraux (2)

1 UCL - Université Catholique de Louvain = Catholic University of Louvain
2 CREM - Centre de recherche en économie et management

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.

Mots clés: Hawkes process; switching regime; Jump diffusion process; self-excited jumps

Domaines: Economies et finances

Donatien Hainaut, Franck Moraux. A switching self-exciting jump diffusion process for stock prices. Annals of Finance, 2019, 15 (2), pp.267-306. ⟨10.1007/s10436-018-0340-5⟩. ⟨halshs-01909772⟩