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Modeling dependency between operational risk losses and macroeconomic variables using Hidden Markov Models

Author

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  • Nikeethan Selvaratnam
  • Dorinel Bastide
  • Cl'ement Fernandes
  • Wojciech Pieczynski

Abstract

Predicting future operational risk losses gives rise to a significant challenge due to the heterogeneous and time-dependent structures present in real-world data. Furthermore, stress test exercises require examining the relationship with operational losses. To capture such relationship, we propose to use an extension of Hidden Markov Models to multivariate observations. This model introduces a third auxiliary variable designed to accommodate the economic covariates in the time-series data. We detail the unique aspects of operational risk data and describe how model calibration is achieved via the Expectation-Maximization (EM) algorithm. Additionally, we provide the calibration results for the various risk-event types and analyze the relevance of the inclusion of the macroeconomic covariates.

Suggested Citation

  • Nikeethan Selvaratnam & Dorinel Bastide & Cl'ement Fernandes & Wojciech Pieczynski, 2026. "Modeling dependency between operational risk losses and macroeconomic variables using Hidden Markov Models," Papers 2604.21734, arXiv.org.
    • Handle: RePEc:arx:papers:2604.21734
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    References listed on IDEAS

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    2. Tsz Chai Fung & Andrei L. Badescu & X. Sheldon Lin, 2019. "Multivariate Cox Hidden Markov models with an application to operational risk," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2019(8), pages 686-710, September.
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    4. Dorinel Bastide & Stéphane Crépey & Samuel Drapeau & Mekonnen Tadese, 2023. "Derivatives’ Risks as Costs in a One-Period Network Model," World Scientific Book Chapters, in: Robert A Jarrow & Dilip B Madan (ed.), Peter Carr Gedenkschrift Research Advances in Mathematical Finance, chapter 8, pages 265-310, World Scientific Publishing Co. Pte. Ltd..
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    6. J. Hambuckers & T. Kneib & R. Langrock & A. Silbersdorff, 2018. "A Markov-switching generalized additive model for compound Poisson processes, with applications to operational loss models," Quantitative Finance, Taylor & Francis Journals, vol. 18(10), pages 1679-1698, October.
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