Bayesian inference, Monte Carlo sampling and operational risk

TLDR

Operational risk is a key quantitative issue driven by Basel II, requiring models that combine internal and external loss data with expert opinion. Following the Loss Distributional Approach, this paper examines three aspects of the Bayesian approach to operational risk modeling. The authors review Bayesian methods for operational risk, including non‑conjugate severity families (g‑and‑h, GB2), Bayesian model selection versus frequentist tests, and stochastic sampling techniques for parameter estimation. They present examples and develop techniques for parameter estimation for general severity and frequency distribution models from a Bayesian perspective.

Abstract

Operational risk is an important quantitative topic as a result of the Basel II regulatory requirements. Operational risk models need to incorporate internal and external loss data observations in combination with expert opinion surveyed from business specialists. Following the Loss Distributional Approach, this paper considers three aspects of the Bayesian approach to the modeling of operational risk. Firstly, we provide an overview of the Bayesian approach to operational risk, before expanding on the current literature through consideration of general families of non-conjugate severity distributions, g-and-h and GB2 distributions. Bayesian model selection is presented as an alternative to popular frequentist tests, such as the Kolmogorov–Smirnov or Anderson– Darling tests. We present a number of examples and develop techniques for parameter estimation for general severity and frequency distribution models from a Bayesian perspective. Finally, we introduce and evaluate recently developed stochastic sampling techniques and highlight their application to operational risk through the models developed.