Operational Risk Management: Optimal Inspection Policy

Abstract

Operational risk is one of the major risks in the financial industry; major banks around the world lost nearly $210 billion from operational risk events between 2011 and 2016 (Huber and Funaro 2018) and inspection on operational risk is required by the Basel Committee on Banking Supervision. Motivated by the importance of operational risk and its current industry regulation, we study how a financial firm can optimally design inspection policies to manage operational risk losses. Specifically, we propose a continuous-time principal-agent model framework to examine a financial firm's (principal) optimal inspection policy and their employees' (agent) effort towards lowering the risk event occurrences. We first consider two commonly used inspection policies, namely, random and periodic policies, and characterize the optimal inspection strategy under each policy. We identify conditions for two different modes of inspection (effort inducement and error correction) as well as nuanced interactions among inspection frequency, penalty charged on errors, and wage paid to employees. We then compare the performances of random and periodic policies. We find that, contrary to conventional wisdom, the random policy is not always optimal; it is dominated by the periodic policy if the inspection cost is sufficiently low. Furthermore, we construct a hybrid policy that strictly dominates random policy and weakly dominates periodic policy, which suggests that a proper reduction of the random element in the inspection policy can always improve its performance. Finally, calibrating model parameters using operational risk data from a major bank in China, we numerically show that our key insights about random, periodic, and hybrid policies are robust to various model extensions.