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A switching self-exciting jump diffusion process for stock prices

Abstract : 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.
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Submitted on : Wednesday, October 31, 2018 - 2:13:44 PM
Last modification on : Monday, February 22, 2021 - 1:54:38 PM
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Donatien Hainaut, Franck Moraux. A switching self-exciting jump diffusion process for stock prices. Annals of Finance, Springer Verlag, 2019, 15 (2), pp.267-306. ⟨10.1007/s10436-018-0340-5⟩. ⟨halshs-01909772⟩

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