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Volatility modelling in a Markov-switching environment: two Ornstein–Uhlenbeck-related approaches

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  • Anita Behme

    (Technische Universität Dresden)

Abstract

We introduce generalisations of the COGARCH model of Klüppelberg et al. (J. Appl. Probab. 41:601–622 2004) and of the volatility and price model of Barndorff-Nielsen and Shephard (J. R. Stat. Soc., Ser. B Stat. Methodol. 63:167–241 2001) to a Markov-switching environment. These generalisations incorporate exogenous jumps of the volatility at the times of a regime switch. Both models are studied within the framework of Markov-modulated generalised Ornstein–Uhlenbeck processes which allows deriving conditions for stationarity, formulas for moments as well as the autocovariance structure of volatility and price process. It turns out that both models inherit various properties of the original models and therefore are able to capture basic stylised facts of financial time series such as uncorrelated log-returns, correlated squared log-returns and non-existence of higher moments in the COGARCH case.

Suggested Citation

  • Anita Behme, 2025. "Volatility modelling in a Markov-switching environment: two Ornstein–Uhlenbeck-related approaches," Finance and Stochastics, Springer, vol. 29(4), pages 1109-1138, October.
    • Handle: RePEc:spr:finsto:v:29:y:2025:i:4:d:10.1007_s00780-025-00567-3
    DOI: 10.1007/s00780-025-00567-3
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    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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