Continuous Time Regime Switching Models and Applications in Estimating Processes with Stochastic Volatility and Jumps
AbstractA regime switching model in continuous time is introduced where a variety of jumps are allowed in addition to the diffusive component. The characteristic function of the process is derived in closed form, and is subsequently employed to create the likelihood function. In addition, standard results of the option pricing literature can be employed in order to compute derivative prices. To this end, the relationship between the physical and the risk adjusted probability measure is explored. The generic relationship between Markov chains and [jump] diffusions is also investigated, and it is shown that virtually any stochastic volatility model model can be approximated arbitrarily well by a carefully chosen continuous time Markov chain. Therefore, the approach presented here can be utilized in order to estimate, filter and carry out option pricing for such continuous state-space models, without the need for simulation based approximations. An empirical example illustrates these contributions of the paper, estimating a stochastic volatility jump diffusion 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 464.
Date of creation: Nov 2002
Date of revision:
Continuous time regime switching; Stochastic volatility jump diffusion; Option pricing; Filtering;
Find related papers by JEL classification:
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2002-12-02 (All new papers)
- NEP-CFN-2002-12-02 (Corporate Finance)
- NEP-ECM-2002-12-10 (Econometrics)
- NEP-ETS-2002-12-02 (Econometric Time Series)
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