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Continuous Time Regime Switching Models and Applications in Estimating Processes with Stochastic Volatility and Jumps

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  • Kyriakos Chourdakis

    (Queen Mary, University of London)

Abstract

A 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.

Suggested Citation

  • Kyriakos Chourdakis, 2002. "Continuous Time Regime Switching Models and Applications in Estimating Processes with Stochastic Volatility and Jumps," Working Papers 464, Queen Mary University of London, School of Economics and Finance.
  • Handle: RePEc:qmw:qmwecw:wp464
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    File URL: http://www.econ.qmul.ac.uk/media/econ/research/workingpapers/archive/wp464.pdf
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    References listed on IDEAS

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    1. Lo, Andrew W & Wang, Jiang, 1995. " Implementing Option Pricing Models When Asset Returns Are Predictable," Journal of Finance, American Finance Association, vol. 50(1), pages 87-129, March.
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    3. Robert A. Jarrow & David Lando & Stuart M. Turnbull, 2008. "A Markov Model for the Term Structure of Credit Risk Spreads," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 18, pages 411-453 World Scientific Publishing Co. Pte. Ltd..
    4. Naik, Vasanttilak, 1993. " Option Valuation and Hedging Strategies with Jumps in the Volatility of Asset Returns," Journal of Finance, American Finance Association, vol. 48(5), pages 1969-1984, December.
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    Cited by:

    1. Patrick Assonken & G. S. Ladde, 2015. "Option Pricing With A Levy-Type Stochastic Dynamic Model For Stock Price Process Under Semi-Markovian Structural Perturbations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(08), pages 1-72, December.
    2. Lim, Andrew E.B. & Watewai, Thaisiri, 2012. "Optimal investment and consumption when regime transitions cause price shocks," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 551-566.

    More about this item

    Keywords

    Continuous time regime switching; Stochastic volatility jump diffusion; Option pricing; Filtering;

    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; Diffusion Processes

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