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A switching self-exciting jump diffusion process for stock prices

Donatien Hainaut () and Franck Moraux ()
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Donatien Hainaut: UCL - Université Catholique de Louvain

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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.

Keywords: self-excited jumps; Hawkes process; switching regime; Jump diffusion process (search for similar items in EconPapers)
Date: 2019-06
New Economics Papers: this item is included in nep-cmp and nep-ets
Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-01909772
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Published in Annals of Finance, Springer Verlag, 2019, 15 (2), pp.267-306. ⟨10.1007/s10436-018-0340-5⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-01909772

DOI: 10.1007/s10436-018-0340-5

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