Stochastic Volatility and Jumps Driven by Continuous Time Markov Chains
AbstractThis 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.
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Bibliographic InfoPaper provided by Queen Mary, University of London, School of Economics and Finance in its series Working Papers with number 430.
Date of creation: Dec 2000
Date of revision:
Option pricing; Markov chain; Moment generating function;
Find related papers by JEL classification:
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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