Robust Estimation of Value-at-Risk through Distribution-Free and Parametric Approaches Using the Joint Severity and Frequency Model: Applications in Financial, Actuarial, and Natural Calamities Domains

Value-at-Risk (VaR) is a well-accepted risk metric in modern quantitative risk management (QRM). The classical Monte Carlo simulation (MCS) approach, denoted henceforth as the classical approach, assumes the independence of loss severity and loss frequency. In practice, this assumption does not always hold true. Through mathematical analyses, we show that the classical approach is prone to significant biases when the independence assumption is...