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

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.