Flexible Expected Shortfall Estimation Using Parametric & Non-Parametric Methods with Applications in Finance, Insurance & Climatology

Abstract

Techniques employing Data fusion concepts are regularly being used in Quantitative Risk Management (QRM) for robust analysis. In our previous work, we studied the most commonly used risk metric of interest, Value-at-Risk $(\mathbf{VaR})$. While VaR is a commonly used risk metric, an alternative risk metric, Expected Shortfall (ES) is well known to have better theoretical properties than VaR. We extend our previous work on studying VaR to include estimating the ES also known as Conditional Value-at-Risk (CVaR). The standard approach of estimating CVaR involves using Monte Carlo simulation (MCS) approach (denoted henceforth as classical approach). This approach involves breaking down the losses into loss severity and loss frequency assuming independence among them. In practice, this assumption may not always hold. To overcome this limitation and handle cases with both light & heavy-tail data, we propose using both a parametric & non-parametric approach. We implement Data-driven Partitioning of Frequency and Severity (DPFS) using K-means Clustering, and Copula-based Parametric modeling of Frequency and Severity (CPFS). These two approaches are verified using simulation experiments on synthetic data and validated on five publicly available datasets from diverse domains. The classical approach estimates CVaR inaccurately for 80% of the simulated data sets and for 60% of the real-world data sets studied in this work. Both the DPFS and the CPFS methodologies attain CVaR estimates within 99% historical bootstrap confidence interval bounds for both simulated and realworld data. Overall, we find that the CPFS method performs better in CVaR estimation for real-world datasets than our previous studies for VaR estimation.