đ€ AI Summary
This study addresses the challenges posed by the heterogeneity and time-varying structure of operational risk losses by proposing a multivariate hidden Markov model (HMM) that incorporates macroeconomic covariates. The approach extends the traditional HMM framework to integrate auxiliary variables and employs the EM algorithm to jointly model time series of multiple types of operational risk events. This formulation effectively captures the dynamic dependence between operational risk and the macroeconomic environment. Empirical results demonstrate that incorporating macroeconomic variables significantly enhances the modelâs relevance and predictive accuracy under stress-testing scenarios, offering a more interpretable and practically useful modeling framework for operational risk management.
đ 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.