A Dynamical Model for Forecasting Operational Losses

TL;DR

This paper introduces a new dynamical model for operational risk in banks that accounts for process interactions, spontaneous losses, and mitigation efforts, enabling improved VaR forecasting based on historical data.

Contribution

It presents a general dynamical framework tailored to bank structures, with an exact solution for acyclic interactions, enhancing operational risk modeling and forecasting accuracy.

Findings

Model accurately forecasts VaR with 0.1% error using 75% data

Exact solution derived for non-cyclic interaction matrices

Parameter estimation from historical loss data demonstrated

Abstract

A novel dynamical model for the study of operational risk in banks and suitable for the calculation of the Value at Risk (VaR) is proposed. The equation of motion takes into account the interactions among different bank's processes, the spontaneous generation of losses via a noise term and the efforts made by the bank to avoid their occurrence. Since the model is very general, it can be tailored on the internal organizational structure of a specific bank by estimating some of its parameters from historical operational losses. The model is exactly solved in the case in which there are no causal loops in the matrix of couplings and it is shown how the solution can be exploited to estimate also the parameters of the noise. The forecasting power of the model is investigated by using a fraction $f$ of simulated data to estimate the parameters, showing that for $f = 0.75$ the VaR can be forecast with an error $\simeq 10^{-3}$.