Paper: arXiv 2604.21734

Authors: Nikeethan Selvaratnam, Dorinel Bastide, Clément 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.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a mathematically solid extension of multivariate Hidden Markov Models incorporating auxiliary macroeconomic variables for operational risk modeling. Its empirical rigor is supported by EM algorithm calibration across risk-event types, though detailed code for full replication is not explicitly provided.

Research Flowchart

  flowchart TD
    A[Research Goal: Model & Stress Test Operational Risk Losses using Macroeconomic Covariates] --> B[Data Inputs: Operational Risk Loss Data & Economic Covariates]
    B --> C[Methodology: Extend Hidden Markov Models to Multivariate Time-Series with Auxiliary Variables]
    C --> D[Model Calibration: Optimize Parameters via Expectation-Maximization Algorithm]
    D --> E[Outcomes: Calibrated HMMs across Risk-Event Types & Validated Macroeconomic Relevance]

Cited References (41)

  1. International Convergence of Capital Measurement and Capital Standards: A Revised Framework — Comprehensive Version (2006) — link
  2. Maximum Likelihood from Incomplete Data via the EM Algorithm (1977)
  3. International Convergence of Capital Measurement and Capital Standards: A Revised Framework ( Basel II ) (2004) — link
  4. Basel III : A Global Regulatory Framework for More Resilient Banks and Banking Systems (2011) — link
  5. Finalising Basel III : In Brief (2017) — link
  6. Common Poisson Shock Models: Applications to Insurance and Credit Risk (2003)
  7. Quantitative Risk Management: Concepts, Techniques and Tools (2015)
  8. Correlated Poisson Processes (2017)
and 33 more
  1. Correlated Multivariate Poisson Processes and Extreme Measures (2017)
  2. A Backward Construction and Simulation of Correlated Poisson Processes (2017)
  3. New Approaches to Operational Risk Modeling (2014)
  4. L 'e vy Copulas: Review of Recent Results (2016)
  5. Simulation and Option Pricing in L 'e vy Copula Models (2019)
  6. Multivariate Models for Operational Risk (2010)
  7. Hidden Markov Regimes in Operational Loss Data: Application to the 2007–2009 Financial Crisis (2016)
  8. Multivariate Cox Hidden Markov Models with an Application to Operational Risk (2019)
  9. A Markov-Switching Generalized Additive Model for Compound Poisson Processes, with Applications to Operational Loss Models (2018)
  10. Operational Risk: A Guide to Basel II Capital Requirements, Models, and Analysis (2011)
  11. The essentials of Risk Management, second edition (2014)
  12. Macroenvironmental Determinants of Operational Losses (2012)
  13. The Impact of the Financial Crisis on Operational Risk in Banks (2011) — link
  14. The Determinants of Reputational Risk in the Banking Sector (2014)
  15. Risk Everywhere: Modeling and Managing Volatility (2018)
  16. An Extreme Value Approach for Modeling Operational Risk Losses Depending on Covariates (2016) — link
  17. 2021 EU-wide stress test – methodological note (2021)
  18. Stress-Test Analytics for Macroprudential Purposes in the euro area (2017)
  19. An Explanatory Note on the Basel II IRB Risk Weight Functions (2005)
  20. A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition (1989) — link
  21. Pattern Recognition and Machine Learning (2006)
  22. Financial Risk Manager Handbook (2011)
  23. Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk (2015) — link
  24. Machine Learning: A Probabilistic Perspective (2012)
  25. Derivatives Risks as Costs in a One‑Period Network Model (2023) — link
  26. Stress Testing and Risk Integration in Banks: A Statistical Framework and Practical Software Guide (2016)
  27. Inference in Hidden Markov Models (2005) — link
  28. Finite Mixture Models (2000)
  29. Exploratory Data Analysis (1977)
  30. A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle (1989) — link
  31. A new look at the statistical model identification (1974)
  32. Estimating the dimension of a model (1978)
  33. Segmentation of Brain MR images through a hidden Markov random field model and the expectation–maximization algorithm (2001)

0 of 41 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.