Pricing Multi-event Triggered Catastrophe Bonds Based on Copula-POT Model

Abstract

The constantly expanding losses caused by frequent natural disasters pose many challenges to the traditional catastrophe insurance market. The purpose of this paper is to develop an innovative framework for pricing catastrophic bonds triggered by multiple events with extreme dependence structure. Due to the bond's low cash flow contingencies and the CAT bond's high return, the multiple-event CAT bond may successfully transfer the catastrophe risk to the huge financial markets to meet the diversification of capital allocations for most potential investors. The designed hybrid trigger mechanism helps reduce moral hazard and improve bond attractiveness with CIR stochastic rate, displaying the co-movement of the wiped-off coupon and principal, the magnitude and intensity of the natural disaster events involved. As the trigger indicators resulted from the potential catastrophic disaster might be associated with heavy tailed margins, nested Archimedean copulas are introduced with marginal distributions modeled by POT-GP distribution for excess data and common parametric models for moderate risks. To illustrate our theoretical pricing framework, we conduct a statistical analysis of pricing a three-event rainstorm CAT bond based on the resulted losses of rainstorms in China during 2006--2020. Monte Carlo simulations are carried out to analyse the sensitivity of the rainstorm CAT bond price in trigger attachment levels, maturity date, catastrophe intensity, and numbers of trigger indicators.