Longstaff利率下巨灾债券定价的一种FFT方法——基于广东省1989~2015台风数据的实证分析

doi:10.12005/orms.2018.0267

运筹与管理 ›› 2018, Vol. 27 ›› Issue (11): 147-156.DOI: 10.12005/orms.2018.0267

Longstaff利率下巨灾债券定价的一种FFT方法——基于广东省1989~2015台风数据的实证分析

马宗刚,郑军,黄金波,袁鲲

广东财经大学金融学院,广东广州 510320

收稿日期:2017-08-25 出版日期:2018-11-25
作者简介:马宗刚(1978-), 男,山东临沂人,讲师,博士,研究方向:金融工程与风险管理;郑军( 1981-) ,贵州铜仁人,男,讲师,博士,研究方向: 金融缔约问题研究;黄金波( 1983-) ,男,河南光山人,副教授,博士,研究方向: 金融风险管理; 袁鲲(1972-),男,湖南益阳人,教授,博士,研究方向:金融工程
基金资助:
国家自然科学基金项目( 71573056,71603058); 教育部人文社会科学研究项目(15YJC790074, 16YJC790033); 广东省自然科学基金项目(2014A030310305,2016A030313656);广东省哲学社会科学规划项目( GD15YYJ06);广东省教育厅2016年科研项目(Z9996005);国家留学基金委地方合作项目支持(201608440451)

An FFT Method for Pricing Catastrophe Bonds with the Longstaff Interest Model Based on Guangdong Province’s Data

MA Zong-gang, ZHENG Jun, HUANG Jin-bo,YUAN Kun

School of Finance,Guangdong University of Finance & Economics, Guangzhou 510320, China

Received:2017-08-25 Online:2018-11-25

摘要/Abstract

摘要： 传统的保险市场难以满足日益频发的巨灾风险分散需求,巨灾债券作为一种非传统金融创新工具提供了一种新的分散机制,而精准定价则对巨灾债券的成功发行与交易起着关键作用。本文基于风险中性测度技术,在Longstaff随机利率且巨灾风险累积损失服从复合泊松损失条件下,得到了零息票巨灾债券价格公式;进一步结合广东省1989~2015年台风风暴潮灾害损失数据进行实证分析;最后,针对定价公式复杂性,本文利用快速傅里叶变换方法进行数值求解,结果验证了本文所构模型的可行性。本文的研究是希望能为我国发行巨灾债券与风险测度提供一定的理论基础与技术支持。

关键词: 巨灾债券, 随机利率, 厚尾分布, 快速傅里叶变换, 广东台风风暴潮损失

Abstract: A limited (and volatile) capacity of traditional reinsurance and retrocession markets can not satisfy the need for diversifying an increasing risk of extreme losses caused by value concentration and climate change. Against this background, an alternative risk transfer (ART) intends to provide additional (re)insurance coverage by transferring insurance risks to the capital market, which offers considerably higher capacities and can thus help satisfy the demand. One of the most prominent ART instruments is catastrophe bonds. Research on pricing of catastrophe risk bonds is not only of great practical significance and urgency, but also has an important academic relevance. Firstly, based on the risk-neutral measure approach, this paper derives a pricing formula of catastrophe bonds in a Longstaff model of the term structure with the hypothesis that the aggregate loss process follows a compound Poisson process. Furthermore, this paper estimates and calibrates the parameters of the pricing model using the loss data caused by storm surge disaster in Guangdong province coastal area with January 1989 - December 2015. As no closed-form solution can be obtained, this paper adopts a fast Fourier transform algorithm to find the numerical solutions for the price of catastrophe risk bonds. Finally, a numerical experiment is conducted to verify the feasibility of this pricing model. The objective of this paper is to provide a theoretical base and technical assistance for issuing China’s catastrophe bonds in the future.

Key words: catastrophe bonds, stochastic interest rate, heavy-detailed distribution, fast Fourier transformation, storm surge disaster loss

中图分类号:

F840.64

马宗刚,郑军,黄金波,袁鲲. Longstaff利率下巨灾债券定价的一种FFT方法——基于广东省1989~2015台风数据的实证分析[J]. 运筹与管理, 2018, 27(11): 147-156.

MA Zong-gang, ZHENG Jun, HUANG Jin-bo,YUAN Kun. An FFT Method for Pricing Catastrophe Bonds with the Longstaff Interest Model Based on Guangdong Province’s Data[J]. Operations Research and Management Science, 2018, 27(11): 147-156.

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Longstaff利率下巨灾债券定价的一种FFT方法——基于广东省1989~2015台风数据的实证分析

An FFT Method for Pricing Catastrophe Bonds with the Longstaff Interest Model Based on Guangdong Province’s Data

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