Application of the convolution operator for scenario integration with loss data in operational risk modeling

Abstract

When using the advanced measurement approach to determine required regulatory capital for operational risk, expert opinion is applied via scenario analysis to help quantify exposure to high-severity events. A methodology is presented that makes use of the convolution operator to integrate scenarios into a baseline model. Using a baseline loss distribution model calibrated on historical losses and a scenario-derived loss distribution calibrated on scenario data points, the addition of both random processes equates to the convolution of the corresponding densities. Using an analogy from digital signal processing, the commutative property of convolution allows one function to smooth and average the other. The inherent uncertainty in scenario analysis has caused concern amongst practitioners when too much emphasis has been placed on absolutes in terms of quantified frequency/severity estimates. This method addresses this uncertainty and produces a combined loss distribution that takes information from the entire domain of the calibrated scenario distribution. The necessary theory is provided within and an example is shown to provide context.

Type
Publication
Journal of Operational Risk (10)
Pavan Aroda
Pavan Aroda
Senior Manager of Operational Risk Modeling and Artificial Intelligence

Pavan is Senior Manager of Operational Risk Modeling and Artificial Intelligence at the Bank of Montreal leading the execution of the Comprehensive Capital Analysis and Review (CCAR) and Dodd-Frank Act Stress Test (DFAST) exercises for US stress testing.  He is responsible for all aspects of model development and performance monitoring of operational risk models used throughout the bank.  He is also tasked with driving BMO’s digital-first strategy and has applied Natural Language Processing (NLP) to simplify and accelerate business processes and continues to utilize machine learning to uncover patterns and derive insight.  He has previously worked in quantitative teams at the national financial regulator, Office of the Superintendent of Financial Institutions (OSFI), and in the cards product division at Canadian Imperial Bank of Commerce (CIBC).

Huaxiong Huang
Huaxiong Huang
Professor

Huaxiong Huang is Professor of Mathematics at the York University. He is VP (Academic) and Executive Director of Research Center of Mathematics (Zhuhai, China). He has served as Deputy Director of the Fields Institute and Director of the Fields Centre for Quantitative Analysis and Modelling. His wide array of publications in applied mathematics focus on fluid mechanics and scientific computing, finance, biology, physiology, energy and medicine.