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Exact solutions for the transient densities of continuous-time Markov switching models: With an application to the poisson multifractal model

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  • Lux, Thomas

Abstract

This paper shows how exact solutions for the transient density of a large class of continuous-time Markov switching models can be obtained. We illustrate the pertinent approach for both simple diffusion models with a small number of regimes as well as for the more complicated so-called Poisson multifractal model introduced by Calvet and Fisher (2001) with an arbitrarily large number of regimes. Our results can be immediately applied as well to various popular Markov switching models in financial economics. Closed-form solutions provide for the possibility of exact maximum likelihood estimation for discretely sampled Markov-switching diffusions and also facilitate the use of such models in applied tasks such as option pricing and portfolio management.

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  • Lux, Thomas, 2013. "Exact solutions for the transient densities of continuous-time Markov switching models: With an application to the poisson multifractal model," Kiel Working Papers 1871, Kiel Institute for the World Economy (IfW Kiel).
    • Handle: RePEc:zbw:ifwkwp:1871
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    References listed on IDEAS

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    1. Lux, Thomas, 2008. "The Markov-Switching Multifractal Model of Asset Returns: GMM Estimation and Linear Forecasting of Volatility," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 194-210, April.
    2. Calvet, Laurent E. & Fearnley, Marcus & Fisher, Adlai J. & Leippold, Markus, 2015. "What is beneath the surface? Option pricing with multifrequency latent states," Journal of Econometrics, Elsevier, vol. 187(2), pages 498-511.
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    Cited by:

    1. Segnon, Mawuli & Lux, Thomas, 2013. "Multifractal models in finance: Their origin, properties, and applications," Kiel Working Papers 1860, Kiel Institute for the World Economy (IfW Kiel).

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    More about this item

    Keywords

    regime switching; continuous-time models; multifractal models;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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