台风风暴潮债券定价——基于我国沿海1989～2015灾害数据

Pricing Typhoon Bonds Based on Storm Surge Disaster in Coastal Areas of China:Based on the Data from 1989 to 2015

随着沿海经济的发展,风暴潮灾害是我国沿海地区面临最主要的自然灾害之一,严重阻碍了经济的可持续发展,而巨灾债券作为一种非传统巨灾风险对冲工具可有效转移巨灾风险。本文基于风险中性测度技术导出了零息票巨灾债券定价公式,并针对重大风暴潮事件造成经济损失的极端特征,采用极值理论中的门限峰值(POT)法研究了风暴潮灾害损失分布的尾部特征。进一步结合我国沿海1989年1月至2015年12月风暴潮直接经济损失数据,研究发现利用门限峰值法重构数据后,广义帕累托分布拟合我国沿海风暴潮损失尾部数据比对数正态、威布尔、伽马等传统厚尾分布拟合效果更好。进而估计并校准了定价模型中的参数,同时给出了一种混合逼近方法对定价模型进行数值求解。最后,数值结果表明巨灾债券价格随着合约期限的增加而减少,随着门限水平的提高而升高,从而验证了定价模型的可行性。

With the development of coastal economics and society, storm surge disaster is one of the most major natural disasters influencing China＇s coastal area, which seriously restricted its sustainable development. This paper derives a zero- coupon typhoon bonds pricing formula in a stochastic interest rates environment with the losses following a compound nonhomogeneous Poisson process. To characterize extreme features in catastrophic storm surge disaster, this paper adopts the Peak Over Threshold（POT） in extreme value theory to characterize the tail characteristics of the loss in catastrophic events. This paper applies extreme value theory to determine the over-threshold peaks of the data, mean excess function plot and sample Hill plot were employed to select the appropriate threshold value and then fits the generalized Pareto distribution to the loss data caused by storm surge disaster in China＇s coastal area with January 1989-December 2015. Furthermore, this paper uses graphics technology,goodness-of-fit tests, and model evaluation to show that the generalized Pareto distribution fits the heavy-tailed distribution better than the Lognormal, Weibull and Gamma distributions in storm surge loss data. And this paper estimates and calibrates the parameters of catastrophe bonds pricing model. As no closed- form solution can be obtained, this paper proposes an approximation algorithm to find the numerical solution for the prices of zero-coupon typhoon bonds. Finally, the numerical results indicate that the catastrophe bond prices decrease as the time to maturity increases, and increase as the threshold level increases, and numerical experiments verify the feasibility of this pricing model.