尖峰厚尾巨灾损失数据的组合分布模型

具有尖峰厚尾特征的巨灾损失数据,通常的损失分布模型很难对其进行拟合,这给巨灾风险管理带来了极大挑战。近几年,关于组合分布模型的研究为巨灾损失数据的拟合提供了一种新的建模思路。组合分布模型是两个普通损失分布的平滑组合。本文将逆威布尔分布分别与帕累托分布和广义帕累托分布进行组合,构建了三个新的组合分布模型,即固定权重的逆威布尔-帕累托组合分布模型、可变权重的逆威布尔-帕累托组合分布模型以及可变权重的逆威布尔-广义帕累托组合分布模型。与现有的组合分布模型相比,这三个组合分布模型结构更加简洁,为拟合尖峰厚尾的巨灾损失数据提供了新的备选模型。     

极值理论POT模型与阈值选取研究

极端值模型是准确估计"厚尾"分布金融资产回报市场风险的有力工具,本文研究了基于GPD分布的极值理论中的POT模型,并通过比较分析各种方法选取的阈值,得出最优的阈值u,最后通过POT模型计算VaR和CVaR值。     

基于POT模型的粮食作物巨灾损失测算——以山东省为例

本文以极值理论的POT模型为基础,利用山东省1949年~2010年的粮食作物单产数据对山东省的粮食作物巨灾损失进行测算。结果表明:极值损失统计模型可以很好的拟合小麦、玉米损失的极值数据,能够有效克服传统统计方法在拟合巨灾风险方面的不足,为农业巨灾风险的评估提供稳健的方法;山东省目前的保险费率较低,与测算的风险水平不一致。本文认为山东省应尽快建立一个完善的巨灾风险准备金制度,为农业巨灾的防灾、救灾和抗灾等积累和筹集资金,以增强农户应对农业巨灾风险的综合实力,实现社会福利的最大化。     

极值理论在金融风险度量中的应用——基于沪深300指数的实证研究

如何准确度量金融市场风险在金融风险管理中扮演着重要角色,而极值理论能对极端风险进行较准确的度量。通过对沪深300指数的实证研究表明,广义帕累托分布能够很好地拟合极端日收益率数据,从而用建立在广义帕累托分布基础上的POT模型来度量投资者所面临的市场风险是合适的。结果显示:基于正态分布假设得到的风险值小于POT模型的风险值。     

数据整合视角下商业银行操作风险度量研究北大核心

随着商业银行改革不断深化,操作风险呈高发态势。整合数据是商业银行准确度量操作风险的基础保证。选取1994—2020年间我国四大国有商业银行1846例操作风险事件,充分利用彼此的损失信息互相补充,结合损失分布法、POT模型以及信度模型对四大商业银行的操作风险进行度量。结果表明:对于一般操作风险损失,对数正态分布的拟合效果优于其他分布;对于极端操作风险损失,POT模型能够较好地对操作风险的尾部进行拟合;分段拟合更能准确描述操作风险的损失特征;运用信度理论可以更准确地对操作风险水平作出合理的估计,弥补数据缺失造成的不足。     

农业保险巨灾风险准备金计提和使用问题研究——以湖南省水稻种植保险为例

本文以湖南省水稻种植保险为例,研究了湖南省农业保险巨灾风险保费准备金提取比例和触发条件。首先,将极值理论引入种植业巨灾损失评估模型,采用超越阈值模型拟合水稻种植保险巨灾损失分布,运用一致性风险度量工具——期望损失,衡量各重现期下巨灾损失程度。然后,结合湖南省水稻种植保险保费数据,提出湖南省种植业保险巨灾准备金提取比例测算方法。实证结果表明,目前湖南地区种植业保险巨灾准备金提取比例较低,但巨灾准备金触发条件设定合理。保险公司应该全面认识农业巨灾损失发生规律,谨慎确定巨灾准备金筹集规模和计提比例,有效防范和应对巨额赔偿风险,保障农业保险稳健经营。     

中国台风巨灾债券利率定价研究——基于均衡定价理论

通过对我国1992年以来损失在1亿元以上的台风损失分布进行拟合,根据我国台风损失数据特征,选择一种能对具有尖峰、厚尾、偏态特征的分布进行较好拟合分布的g-h分布进行分析;在均衡定价理论的基础上构建一种台风巨灾债券利率定价模型,并利用相关数据进行定价分析,将模型应用于三种台风巨灾债券并计算出其利率。结果表明,无论是哪种类型的巨灾债券,由于利率均高于同期国债利率,对投资者来说都具有较大吸引力,是一种较为理想的巨灾风险创新产品。     

巨灾风险保险市场失灵与对策理论

巨灾风险保险市场存在需求周期性变化、较高价格敏感度和较低收入弹性、偏爱低免赔额和折扣保单、依赖政府慈善等多种失灵现象。传统经济学认为主要原因在于巨灾风险的非独立性和损失的重尾分布、投保人的逆选择与道德风险、巨灾风险保险的准公共物品性质等;新经济学则从保险人的"模糊性厌恶"、投保人的"可得性偏差"、"显著性思维"、政府"大灾必救"的福利制度等方面作出新的解释。解决失灵的对策关键在于分散巨灾风险重尾部分的损失。     

基于有限理性的农业巨灾保险主体行为分析及优化

基于有限理性的进化博弈分析框架,本文分析了农业巨灾保险主体群落基因复制动态变化过程。研究发现,农民个体是否购买农业巨灾保险关键取决于个体的比较预期收益和其所要承担选择成本的大小。而保险公司与投保农民的博弈轨迹不存在使博弈双方共同稳定的进化稳定策略,只能实现农业巨灾保险市场上平均意义上较优策略。同时,由于农业巨灾风险强破坏性和发生概率分布厚尾性的影响,政府的有效行为具有优化农业巨灾保险主体行为变迁轨迹的效能。     

基于资产负债管理的我国巨灾再保险定价研究

我国是自然灾害种类多、频率高、损失大的国家。对巨灾保险需求很大,但是由于巨灾的特性,给保险公司带来的风险极大,因此对巨灾再保险有很大需求。通过建立资产、负债和利率模型,根据我国洪水、暴雨损失程度和频率拟合关系式,采用蒙特卡罗模拟分别计算有无违约风险和发行巨灾债券的巨灾再保险费率。通过计算结果看出,发行巨灾债券能够降低违约风险,提高巨灾再保险费率,增加巨灾再保险合同的价值。同时,还考虑了资产负债比、免赔额、债券价值与负债占比对巨灾再保险费率的影响并得到合理结果。本文根据我国洪水、暴雨实际发生情况,从资产负债管理视角研究巨灾再保险定价问题,对于开展适合中国国情的巨灾再保险具有理论指导意义。     

Modeling claims data with composite Stoppa models

In this paper, a new class of composite model is proposed for modeling actuarial claims data of mixed sizes. The model is developed using the Stoppa distribution and a mode-matching procedure. The use of the Stoppa distribution allows for more flexibility over the thickness of the tail, and the mode-matching procedure gives a simple derivation of the model compositing with a variety of distributions. In particular, the Weibull–Stoppa and the Lognormal–Stoppa distributions are investigated. Their performance is compared with existing composite models in the context of the well-known Danish fire insurance data-set. The results suggest the composite Weibull–Stoppa model outperforms the existing composite models in all seven goodness-of-fit measures considered.     

Pricing catastrophe risk in life (re)insurance

What is the catastrophe risk a life insurance company faces? What is the correct price of a catastrophe cover? During a review of the current standard model, due to Strickler, we found that this model has some serious shortcomings. We therefore present a new model for the pricing of catastrophe excess of loss cover (Cat XL). The new model for annual claim cost C is based on a compound Poisson process of catastrophe costs. To evaluate the distribution of the cost of each catastrophe, we use the Peaks Over Threshold model for the total number of lost lives in each catastrophe and the beta binomial model for the proportion of these corresponding to customers of the insurance company. To be able to estimate the parameters of the model, international and Swedish data were collected and compiled, listing accidents claiming at least twenty and four lives, respectively. Fitting the new model to data, we find the fit to be good. Finally we give the price of a Cat XL contract and perform a sensitivity analysis of how some of the parameters affect the expected value and standard deviation of the cost and thus the price.     

Composite Lognormal–Pareto model with random threshold

This paper further considers the composite Lognormal–Pareto model proposed by Cooray & Ananda (2005) and suitably modified by Scollnik (2007). This model is based on a Lognormal density up to an unknown threshold value and a Pareto density thereafter. Instead of using a single threshold value applying uniformly to the whole data set, the model proposed in the present paper allows for heterogeneity with respect to the threshold and let it vary among observations. Specifically, the threshold value for a particular observation is seen as the realization of a positive random variable and the mixed composite Lognormal–Pareto model is obtained by averaging over the population of interest. The performance of the composite Lognormal–Pareto model and of its mixed extension is compared using the well-known Danish fire losses data set.     

我国巨灾风险可保性的理性思考

巨灾保险虽然一直未能真正踏上破冰之旅,但近年频发加剧的巨灾,使巨灾保险再次成为保险业的聚焦领域。巨灾风险可保性争论不休,业界徘徊不前,厘清巨灾风险的保险属性,可否引导市场参与巨灾风险的有效管理,特别是金融市场、保险市场和资本市场的联动推进,更是尚需解决的问题。基于巨灾风险管理的理论分析认为,我国巨灾风险具备可保性有其理...     

The risk implications of insurance securitization: The case of catastrophe bonds

Catastrophe (Cat) bonds are insurance securitization vehicles which are supposed to transfer catastrophe-related underwriting risk from issuers to capital markets. This paper addresses key, unanswered questions concerning Cat bonds and offers the following results. First, our findings show firms that issue Cat bonds exhibit less risky underwriting portfolios with less exposure to catastrophe risks and overall less need to hedge catastrophe risk. These results show that the access to the market for insurance securitization is easiest for firms with less risky portfolios. Second, firms that issue Cat bonds are found to experience a reduction in their default risk relative to non-issuing firms and our results, therefore, demonstrate that Cat bonds provide effective catastrophe hedging for issuing firms. Third, firms with less catastrophe exposure, increase their catastrophe exposure following an issue. Therefore, our paper cautions that the ability to hedge catastrophe risk causes some firms to seek additional catastrophe risk.     

巨灾风险证券化中的操作风险及其控制途径

巨灾风险证券化是把巨灾保险风险转化为衍生证券,销售给金融市场上的投资者,以此实现巨灾保险风险向资本市场的分散转移。但受信息不对称、触发机制等因素影响,巨灾风险证券化这种复杂的技术手段也会引起一些操作风险,如道德风险、基差风险、信用风险等。通过完善信息披露机制、合理选择触发方式、强化巨灾证券的交易保证金要求、加强监管等措施,可以有效地降低巨灾风险证券化过程中的各种风险,促进其平稳健康发展。     

A Note: Natural Generalization of Black-Scholes in the Presence of Skewness,Using Stable Processes

The Lognormal price model is generalized to the class of Log-Stable Processes, a family which possesses self-similarity properties usually only associated with the Lognormal, but which, more generally, can model negatively skewed distributions of return. This generalization appears to explain several discrepancies between the Black-Scholes Model and observed market phenomena, such as the variation of implied volatility of option price with exercise price and term to expiry, and the nonzero probability of bankruptcy or ‘crash’. It will be argued that the class of maximally negatively skewed Stable distributions (a class which, paradoxically, contains the normal) may be utilized to produce models which imply these phenomena naturally.     

(Non-)robustness of maximum likelihood estimators for operational risk severity distributions

The quality of operational risk data sets suffers from missing or contaminated data points. This may lead to implausible characteristics of the estimates. Outliers, especially, can make a modeler's task difficult and can result in arbitrarily large capital charges. Robust statistics provides ways to deal with these problems as well as measures for the reliability of estimators. We show that using maximum likelihood estimation can be misleading and unreliable assuming typical operational risk severity distributions. The robustness of the estimators for the Generalized Pareto distribution, and the Weibull and Lognormal distributions is measured considering both global and local reliability, which are represented by the breakdown point and the influence function of the estimate.     

非寿险承保风险引发系统性风险的复杂网络分析

本文基于我国财险业2009~2018年数据,用复杂网络理论模型构建了财险业承保业务网络,并模拟了承保风险传染过程,分析了承保风险对财险业系统性风险的影响轨迹及程度。研究发现,我国财险业承保业务网络的联系越来越密切,承保风险的增加会引发传染风险,进而导致爆发系统性风险。但当前我国财险业整体稳定,只有发生1600亿元及以上的初始损失时,才会有保险机构陷入危机;当初始损失大于8500亿元时,才会有保险机构因传染风险而陷入危机。在承保风险的传染过程中,损失至少以数倍的速度下降;保险机构主要在承保风险和前两轮传染中损失较大,在后续传染轮次陷入危机的可能性极低。因此,防范巨灾风险、监管重点公司、探索巨灾转移机制并建立承保风险预警机制显得比较重要。