融合风险比率的双触发巨灾看跌期权及其定价  

Double-triggered catastrophe put option with risk ratio and its pricing

作　　者：李世龙 刘茜 LI Shilong;LIU Xi(Insurance Institute,Shandong University of Finance and Economics,Jinan 250014,Shandong,China)

机构地区：[1]山东财经大学保险学院,山东济南250014

出　　处：《山东大学学报(理学版)》2025年第3期12-21,40,共11页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(72171133);山东省自然科学基金资助项目(ZR2020MA036)。

摘　　要：在普通双触发巨灾看跌期权支付结构中融入基于在险价值(value at risk,VaR)的风险比率,以体现保险公司累积巨灾赔付损失对巨灾期权行权收益的影响和保险公司的风险承受水平。首先,在金融与巨灾乘积概率空间下推导出融合风险比率巨灾看跌期权的定价公式;其次,基于超阈值模型(peak over threshold,POT)模型拟合我国台风的巨灾损失分布以体现巨灾损失的厚尾性特征;最后,利用蒙特卡罗模拟方法对影响巨灾看跌期权的相关因素进行敏感性分析,并与普通巨灾期权进行比较。In order to reflect both the impact of the accumulated catastrophe compensation loss of insurance companies on the exercise returns of catastrophe options and the risk tolerance level of insurance companies,the risk ratios based on VaR is added into the payment structure of ordinary double triggered catastrophe put options.Firstly,the pricing formula for catastrophe put options with risk ratios is derived in the product probability space of finance and catastrophe;Secondly,the POT model is utilized to fit the distribution of catastrophe loss based on the typhoon catastrophe data in China to display the thick tailed characteristics of catastrophic losses;Finally,the Monte Carlo simulation method is used to analyze the sensitivity of the factors affecting the catastrophe put option and the prices of the catastrophe put options with risk ratios are compared with those of ordinary catastrophe options.

关 键 词：风险比率 双触发巨灾看跌期权 乘积概率空间 超阈值模型 

分 类 号：O211.9[理学—概率论与数理统计] F224.7[理学—数学]