Risk Analysis of Rice Losses Caused by Typhoon for Taiwan

Abstract

This paper applies extreme value theory to the Taiwanese rice loss caused by typhoons to demonstrate how these new statistical tools can be used to improve quantitative risk management. The application of the extreme value theory to statistics allowed us to test models with data from the upper tail of a distribution. Using the block-max and peak-over-threshold approaches to extreme value modeling, we matched generalized extreme value distribution (GEVD) and generalized Pareto distribution (GPD) to agricultural losses caused by natural disasters, with Taiwanese data from 1971 to 2005. We then evaluated the appropriateness of the upper tail fitting to loss data by comparing with standard parametric modeling that is based on lognormal and gamma distributions. The extreme value theory outperforms classical parametric fits for the largest observed historical losses. Finally, we draw particular attention to issues related to agricultural disaster and calculate the 90th, 95th, and 99th percentile of VaR and expected shortfall. These results could help the authorities or agriculture risk managers to check the applicable loss-compensation regulations. Keywords: Generalized Extreme Value Distribution, Generalized Pareto Distribution, T-Year Return Level, Value-at-Risk, Expected Shortfall