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

TL;DR

This paper introduces an extended Hidden Markov Model incorporating macroeconomic variables to better predict operational risk losses and facilitate stress testing.

Contribution

It presents a novel multivariate HMM extension with an auxiliary variable for economic covariates, calibrated via EM algorithm, tailored for operational risk data.

Findings

Model effectively captures heterogeneity and time dependence in operational risk data.

Inclusion of macroeconomic covariates improves risk loss predictions.

Calibration results vary across different risk-event types.

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.