Flexible estimation of risk metric using copula model for the joint severity-frequency loss framework

Predictive analytics and data fusion techniques are being regularly used for analysis in Quantitative Risk Management (QRM). The primary risk metric of interest, Value-at-Risk (VaR), has always been difficult to robustly estimate for different data types. The classical Monte Carlo simulation (MCS) approach (denoted henceforth as classical approach) assumes the independence of loss severity and loss frequency. In practice, this assumption may not always hold. To overcome this limitation and more robustly estimate the corresponding VaR, we propose a new approach known as Copula-based Parametric Modeling of Frequency and Severity (CPFS). The proposed approach is verified via large-scale MCS experiments and validated on three publicly available datasets. We compare CPFS with the classical approach and a Data-driven Partitioning of Frequency and Severity (DPFS) approach for robust VaR estimation. We observe that the classical approach estimates VaR poorly while both the DPFS and the CPFS methodologies attain VaR estimates for real-world data. These studies provide real-world evidence that the CPFS and DPFS methodologies have merits for its use to accurately estimate VaR.