Robust estimation of value-at-risk through correlated frequency and severity model

In this article we develop a novel method for accurately estimating the Value-at-Risk (VaR) in the context of modern Operational Risk Management (ORM). We develop a method called Data Partition of Frequency and Severity (DPFS) which more accurately computes the VaR in a modern ORM context. The DPFS involves using clustering analysis to partition the frequency and severity components of the loss data. Since the fundamental theory of modern ORM implicitly assumes a “correlation” between frequency and severity of losses, we argue that this approach should follow naturally. To test this idea, we perform simulation based studies which show that in a theoretical situation, the new DPFS method will perform better than and in worst case as well as the current VaR best practices (which we call “classical” method). In addition, we implement our methodology on two publicly available datasets: (1) Financial Index data of S&P 500; (2) Chemical Loss spills as tracked by the US National Coast Guard. We observe that the “classical” VaR calculation inaccurately estimates the data in both the simulation and real-world data studies while DPFS attains much more accurate VaR estimates.