巨灾风险度量与保险衍生品定价方法研究
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摘要
自从上个世纪九十年代以来,由于巨灾损失发生频率和强度的不断加大,保险公司仅仅依靠自身的实力再也无法消化自身所面临的风险.在这种情况下,巨灾保险期货、巨灾保险期权,巨灾债券等巨灾保险衍生品应运而生.而且,最近几年,保险衍生品的快速发展导致了人寿保险衍生品和天气衍生品等非巨灾新型保险衍生品的出现.因此,对保险衍生证券定价问题的研究不仅具有重大的理论价值,同时也具有十分重要的现实意义.
本文的研究包含三部分内容:首先研究了巨灾风险度量和巨灾超额损失再保险合同定价的方法;其次讨论了巨灾保险衍生品定价的方法,这是本文的核心部分;最后研究了人寿保险衍生品的定价方法.本文的主要内容如下:
第一章系统地阐述了保险定价方法与金融定价方法的差异与联系.
第二章全面介绍了一些主要保险衍生品的运行机制、特点,以及目前定价的主要方法.
第三章首先基于指数回归模型构造了厚尾分布的一个Hall分布族的极值分位数估计,对巨灾风险进行了度量;其次通过隐含风险中性分布对巨灾超额损失再保险合同进行了定价.同时,结合Weibull极值分布和超额损失再保险的特征,给出了巨灾超额损失再保险合同定价的闭型表达式.
第四章首先将超出随机门限值方法应用于巨灾保险衍生品的定价,建立了主要针对大损失小概率索赔的统计定价框架,得到了一系列巨灾保险衍生品定价的显式解;其次,在标的物不可交易的框架下,讨论了一种为保险连接证券估值的简单可行的套利方法,得到了在全部损失情形下巨灾债券估值的闭型表达式.
第五章首先引入了一种基于退休年金的欧式看涨期权,通过建立相关的精算模型对一些特定情形进行了定价,并与传统的退休金合约进行了比较;其次,我们引入了一种为长寿债券建模和定价的方法,通过年金市场报价获得隐含生存概率,从而得到长寿债券的价格动态变化机制.
本文研究的目的主要是为保险公司的安全有效营运和资本市场上投资者进行理性投资提供决策依据.通过保险衍生证券保险公司可以将本身无法应对的风险转移到资金雄厚的资本市场,增强营运的稳定性.同时也使得资本市场上投资者的选择更加多样化,从而降低投资者面临的系统风险.因此,对保险衍生证券定价问题的研究又具有十分重要的应用价值,当然也实现了经济理论和精算理论与实务的有机结合.
Since the 1970s the frequency and severity of catastrophe have been increased so great that the insurance companies can not take the catastrophic risk only by themselves. Just in this situation, catastrophe insurance products such as CAT futures, CAT options, CAT bonds began to appear. In the recent years, the rapid development of catastrophic insurance derivatives caused the new non-catastrophic insurance derivatives such as life insurance derivatives and weather insurance derivatives, to come forth.Therefore, research on the insurance derivatives pricing has great significance on both economic theory and practice.
This thesis consists of three parts. The first part investigates the methods to measure the catastrophic risk and pricing for the catastrophic excess-of-loss reinsurance contracts. The Second part presents some new methods to pricing for catastrophic insurance derivatives, which is the core of the thesis. The last part studies the pricing methods to the life insurance derivates.The main contents are as follows:
Chapter 1 makes a systematic exposition of the differences and relationships between insurance pricing methods and financial pricing methods.
Chapter 2 introduces comprehensively the operation mechanism, characteristics, and present pricing methods to the insurance derivatives.
In Chapter 3,firstly,we construct a high quantile estimator of a heavy-taileddistribution subclass------Hall distribution class based on exponential regressionmodel.Risk of catastrophic insurance is measured. Secondly, we pricing for the catastrophic excess-of-loss reinsurance contract by virtue of the implied risk neutral distributions.At the same time, a closed expression to the pricing of catastrophic excess-of-loss reinsurance is presented while considering the feature of Weibull distribution and excess-of-loss reinsurance contract.
In Chapter 4, we introduce the PORT method to the field of catastrophic insurance derivatives pricing, and establish a statistical pricing systematic framework which is particularly emphasized on the claims with low frequency and large losses. A series of explicit form solution to catastrophic insurance derivatives pricing is obtained. In the last, we develop a simple arbitrage approach to valuing the insurance-linked securities notwithstanding in the framework of non-traded underlying. A closed-form valuation expression is given in the case of pure crashes.
In Chapter 5, we introduce a European call option on pension annuity. The pricing principle for some particular cases is illustrated by setting up the corresponding actuarial model. What's more, the call option is compared with traditional pension contracts. Second, we present a methodology for the modeling and pricing of longevity bonds. We show how to derive implied survival probabilities from annuity market quotes.The price dynamics of longevity bonds is obtained.
The main aim of the thesis is to provide decision-making support for the insurance companies to run safely and efficiently, and for the investors in financial markets to make rational investment. By virtue of insurance derivatives insurance companies can transfer the risk that they can not take only by themselves to capital markets. Therefore, it strengthens the stability to run for insurance company. What's more, it diversifies the choices of investors and reduces investors' systematic risk. In all, research on insurance derivatives pricing is very meaningful to application. Of course, economic theory and actuarial theory combine with practical business organically.
本文的研究包含三部分内容:首先研究了巨灾风险度量和巨灾超额损失再保险合同定价的方法;其次讨论了巨灾保险衍生品定价的方法,这是本文的核心部分;最后研究了人寿保险衍生品的定价方法.本文的主要内容如下:
第一章系统地阐述了保险定价方法与金融定价方法的差异与联系.
第二章全面介绍了一些主要保险衍生品的运行机制、特点,以及目前定价的主要方法.
第三章首先基于指数回归模型构造了厚尾分布的一个Hall分布族的极值分位数估计,对巨灾风险进行了度量;其次通过隐含风险中性分布对巨灾超额损失再保险合同进行了定价.同时,结合Weibull极值分布和超额损失再保险的特征,给出了巨灾超额损失再保险合同定价的闭型表达式.
第四章首先将超出随机门限值方法应用于巨灾保险衍生品的定价,建立了主要针对大损失小概率索赔的统计定价框架,得到了一系列巨灾保险衍生品定价的显式解;其次,在标的物不可交易的框架下,讨论了一种为保险连接证券估值的简单可行的套利方法,得到了在全部损失情形下巨灾债券估值的闭型表达式.
第五章首先引入了一种基于退休年金的欧式看涨期权,通过建立相关的精算模型对一些特定情形进行了定价,并与传统的退休金合约进行了比较;其次,我们引入了一种为长寿债券建模和定价的方法,通过年金市场报价获得隐含生存概率,从而得到长寿债券的价格动态变化机制.
本文研究的目的主要是为保险公司的安全有效营运和资本市场上投资者进行理性投资提供决策依据.通过保险衍生证券保险公司可以将本身无法应对的风险转移到资金雄厚的资本市场,增强营运的稳定性.同时也使得资本市场上投资者的选择更加多样化,从而降低投资者面临的系统风险.因此,对保险衍生证券定价问题的研究又具有十分重要的应用价值,当然也实现了经济理论和精算理论与实务的有机结合.
Since the 1970s the frequency and severity of catastrophe have been increased so great that the insurance companies can not take the catastrophic risk only by themselves. Just in this situation, catastrophe insurance products such as CAT futures, CAT options, CAT bonds began to appear. In the recent years, the rapid development of catastrophic insurance derivatives caused the new non-catastrophic insurance derivatives such as life insurance derivatives and weather insurance derivatives, to come forth.Therefore, research on the insurance derivatives pricing has great significance on both economic theory and practice.
This thesis consists of three parts. The first part investigates the methods to measure the catastrophic risk and pricing for the catastrophic excess-of-loss reinsurance contracts. The Second part presents some new methods to pricing for catastrophic insurance derivatives, which is the core of the thesis. The last part studies the pricing methods to the life insurance derivates.The main contents are as follows:
Chapter 1 makes a systematic exposition of the differences and relationships between insurance pricing methods and financial pricing methods.
Chapter 2 introduces comprehensively the operation mechanism, characteristics, and present pricing methods to the insurance derivatives.
In Chapter 3,firstly,we construct a high quantile estimator of a heavy-taileddistribution subclass------Hall distribution class based on exponential regressionmodel.Risk of catastrophic insurance is measured. Secondly, we pricing for the catastrophic excess-of-loss reinsurance contract by virtue of the implied risk neutral distributions.At the same time, a closed expression to the pricing of catastrophic excess-of-loss reinsurance is presented while considering the feature of Weibull distribution and excess-of-loss reinsurance contract.
In Chapter 4, we introduce the PORT method to the field of catastrophic insurance derivatives pricing, and establish a statistical pricing systematic framework which is particularly emphasized on the claims with low frequency and large losses. A series of explicit form solution to catastrophic insurance derivatives pricing is obtained. In the last, we develop a simple arbitrage approach to valuing the insurance-linked securities notwithstanding in the framework of non-traded underlying. A closed-form valuation expression is given in the case of pure crashes.
In Chapter 5, we introduce a European call option on pension annuity. The pricing principle for some particular cases is illustrated by setting up the corresponding actuarial model. What's more, the call option is compared with traditional pension contracts. Second, we present a methodology for the modeling and pricing of longevity bonds. We show how to derive implied survival probabilities from annuity market quotes.The price dynamics of longevity bonds is obtained.
The main aim of the thesis is to provide decision-making support for the insurance companies to run safely and efficiently, and for the investors in financial markets to make rational investment. By virtue of insurance derivatives insurance companies can transfer the risk that they can not take only by themselves to capital markets. Therefore, it strengthens the stability to run for insurance company. What's more, it diversifies the choices of investors and reduces investors' systematic risk. In all, research on insurance derivatives pricing is very meaningful to application. Of course, economic theory and actuarial theory combine with practical business organically.
引文
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