基于指数效用函数的零息巨灾债券无差异定价  

Undifferentiated Pricing for Zero-coupon Catastrophe Bonds Based on Exponential Utility

作　　者：刘静 肖宇谷 曾宇哲 LIU Jing;XIAO Yugu;ZENG Yuzhe

机构地区：[1]中国人民大学财政金融学院保险系 [2]中国人民大学统计学院风险管理与精算教研室 [3]中国人民大学统计学院

出　　处：《保险研究》2018年第8期35-46,共12页Insurance Studies

基　　金：国家社科基金重大项目(16ZDA052):巨灾保险的精算统计模型及其应用研究;教育部人文社会科学重点研究基地重大项目(16JJD910001):基于大数据的精算统计模型与风险管理问题研究;中国人民大学2018年度"中央高校建设世界一流大学(学科)和特色发展引导专项资金"

摘　　要：巨灾经常对保险行业产生巨大冲击,也催生了巨灾债券市场。但巨灾债券的复杂性和非流动性特征,对巨灾债券定价带来了很大的困难,以至于目前还没有统一的定价方法,特别是由于巨灾债券市场还远不完备,不适合采用经典的无套利定价方法。本文应用无差异定价方法,假设买方(投资者)具有指数效用函数,给出了零息巨灾债券无差异价格的解析表达式。同时本文在股票价格与巨灾风险指数为正相依的情况下,对无差异价格进行了敏感性分析,得到了一些有意义的结果。Catastrophes （CAT） occur more and more frequently in recent decades,which produces a huge impacton the development of the insurance industry. Along this trend, the CAT bond market has emerged and become siza-ble. In view of some characteristics such as complexity and illiquidity of this market, pricing CAT bonds is a challenging task. So far various approaches have been proposed, but they are very different and far from being unified. Due to the incompleteness of the CAT bond market, the prevailing non-arbitrage pricing theory does not work well. In this paper,we studied the undifferentiated pricing method for CAT bonds. Assuming a buyer （investor） having an exponential utility, we derived a formula for the undifferentiated price of a zero-coupon CAT bond, and conducted some sensitivity analyses on condition that share prices were positively correlated to CAT risk index. The results are of some reference value.

关 键 词：巨灾债券 无差异定价 指数效用函数 几何布朗运动 相依二项模型 

分 类 号：F840.64[经济管理—保险]