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A self-exciting switching jump diffusion: properties, calibration and hitting time

By Donatien Hainaut and Griselda Deelstra

Abstract

A way to model the clustering of jumps in asset prices consists in combining a diffusion process with a jump Hawkes process in the dynamics of the asset prices. This article proposes a new alternative model based on regime switching processes, referred to as a self-exciting switching jump diffusion (SESJD) model. In this model, jumps in the asset prices are synchronized with changes of states of a hidden Markov chain. The matrix of transition probabilities of this chain is designed in order to approximate the dynamics of a Hawkes process. This model presents several advantages compared to other jump clustering models. Firstly, the SESJD model is easy to fit to time series since estimation can be performed with an enhanced Hamilton filter. Secondly, the model explains various forms of option volatility smiles. Thirdly, several properties about the hitting times of the SESJD model can be inferred by using a fluid embedding technique, which leads to closed form expressions for some financial derivatives, like perpetual binary options.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Topics: Sciences actuarielles, Jump diffusion, Self-exciting process, Switching process
Publisher: 'Informa UK Limited'
Year: 2018
DOI identifier: 10.1080/14697688.2018.1501511
OAI identifier: oai:dipot.ulb.ac.be:2013/280669
Provided by: DI-fusion
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