Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/330387 
Authors: 
Year of Publication: 
2025
Citation: 
[Journal:] Finance and Stochastics [ISSN:] 1432-1122 [Volume:] 29 [Issue:] 4 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2025 [Pages:] 1109-1138
Publisher: 
Springer, Berlin, Heidelberg
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.
Subjects: 
Stochastic volatility
Regime switching
Continuous-time GARCH model
Markov-modulated GOU process
Lévy processes
JEL: 
C02
C62
E37
G17
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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