Stochastic Volatility and Jumps Driven by Continuous Time Markov Chains

Kyriakos Chourdakis

No 430, Working Papers from Queen Mary University of London, School of Economics and Finance

Abstract: This paper considers a model where there is a single state variable that drives the state of the world and therefore the asset price behavior. This variable evolves according to a multi-state continuous time Markov chain, as the continuous time counterpart of the Hamilton (1989) model. It derives the moment generating function of the asset log-price difference under very general assumptions about its stochastic process, incorporating volatility and jumps that can follow virtually any distribution, both of them being driven by the same state variable. For an illustration, the extreme value distribution is used as the jump distribution. The paper shows how GMM and conditional ML estimators can be constructed, generalizing Hamilton's filter for the continuous time case. The risk neutral process is constructed and contigent claim prices under this specification are derived, in the lines of Bakshi and Madan (2000). Finally, an empirical example is set up, to illustrate the potential benefits of the model.

Keywords: Option pricing; Markov chain; Moment generating function (search for similar items in EconPapers)
JEL-codes: C51 G12 G13 (search for similar items in EconPapers)
Date: 2000-12-01
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:qmw:qmwecw:430

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