基于POT-GPD模型的地震巨灾风险测度

依据极值理论构建基于GPD的POT模型,对我国1969年至2013年间地震直接经济损失数据进行拟合;选取恰当的阀值,并对模型形状参数及尺度参数进行估计,以此研究地震巨灾损失的尾部特征,从而合理的对地震巨灾风险进行度量,得到损失数据的高分位数;最后,探讨了POT模型在再保险的高超额层选取及定价问题中的应用.     

基于POT模型的巨灾风险度量与保险模式研究——以地震风险为例

巨灾风险发生的频率低且损失大,具有显著的厚尾性特征,因此不易度量其风险。本文以地震风险为例,采用1961-2011年以来中国发生的4.5级以上地震造成的损失值作为样本,在进行物价调整之后引入了POT模型和广义Pareto分布对损失数据进行拟合,计算出不同的置信度水平下不同的VaR值,得到不同的保费规模与地震保险的价格,并以此为依据设计我国巨灾保险的风险分散机制。     

基于分位数回归模型的地震巨灾风险评估

地震损失数据存在明显的厚尾特征,使得通常的均值回归模型因为容易受到极端值的影响而无法适用。本文对传统的分位数回归模型和函数系数的分位数回归模型进行了比较研究,分析了它们的优缺点,并基于我国大陆地区1990-2015年的地震灾害损失数据,重点探讨了它们在我国地震巨灾风险管理中的应用,计算了不同震级和置信水平下,我国地震灾害损失的VaR和TVaR等风险度量值。基于前述结果,本文最后还探讨了我国地震巨灾指数保险的设计和费率厘定问题。     

中国非金融行业上市公司现金流风险研究

本文研究了我国非金融行业上市公司经营净现金流的风险状况,建立了风险现金流(Cash-Flow-at-Risk)的POT模型,在可比公司估计的分析框架下,度量并分析经营净现金流风险。实证结果表明:第一、房地产业和综合类风险现金流级别相对最高,而采掘业、交通运输仓储业、电力煤气及水的生产与供应业的风险现金流相对最低;第二、除房地产业和综合类业外,其他行业ST公司风险现金流值均比同行业正常公司值要高;第三、受金融危机的影响,与2006、2007年同期相比,2008年经营净现金流为负值公司数目及超出风险现金流值的公司数目均明显增加。     

一类巨灾风险—地震灾害债券的设计

巨灾保险风险证券化是国际上分散巨灾风险的一项金融保险创新.对我国而言,发展巨灾保险风险证券化最适宜的证券品种是巨灾债券.收集1969~2004年我国地震直接经济损失在9900万元以上的损失数据,利用非寿险精算技术分析我国地震损失分布和次数,并在此基础上利用CAPM和债券定价原理计算地震灾害债券的收益率和价格,从而对地震灾害债券作了初步设计.     

强混合样本下单参数指数族参数的平均化经验贝叶斯估计

本文在强混合样本下,利用平均化的思想,研究了一类单参数指数族参数的经验贝叶斯估计,在一定假设条件下得到了该经验贝叶斯估计收敛速度.推广了之前文献的结果,同时,在β混合样本下对该经验贝叶斯估计的风险与贝叶斯估计的风险之间的差值进行了数值模拟.     

基于POT方法的商业银行操作风险极端值估计

对于商业银行而言,操作风险已经成为与市场风险和信用风险同样重要的风险。本文利用极值理论超越样本的估计能力,采用极值理论中对数据要求量较少,可以进行单步预测的超阈值(POT)方法对我国商业银行操作损失极端值分布进行估计,以均值超额函数图和拟合直线的交点确定阈值,估计出给定置信水平之下操作风险损失的分位数,从而使得国内商业银行操作风险监管资本的计算成为可能。     

基于贝叶斯极值估计的商业银行内部欺诈风险度量研究

内部欺诈风险是我国商业银行面临的一个重大风险来源。本文针对内部欺诈具有的低频率高损失的特点,采用不同分布分段刻画其损失统计分布规律,对于低于和高于门限值的样本点,采用Box-Cox变换和全Paretian分布模型进行分析,然后采用贝叶斯估计对全Paretian分布模型的参数进行估计,接着在此基础上对建立了一个内部欺诈风险度量模型,然后使用所构建的风险度量模型对操作风险在险风险值、经济资本和最大可能损失进行了测算,最后提出了防范操作风险的政策建议。     

极值理论及其在巨灾再保险定价中的应用

巨灾损失中往往存在极端值,一般统计分布对其拟合效果欠佳,本文运用极值理论对极端值建模,基于分层定价的思想,在不同的起赔点下对再保险超额损失部分的定价进行了探讨,并以洪水损失数据为例进行了实证研究,拟合了POT模型,得到了洪水再保险纯保费。     

帕累托索赔分布中风险参数的经验贝叶斯估计

本文建立了贝叶斯模型,讨论了帕累托索赔额分布中参数的估计问题,得到了风险参数的极大似然估计、贝叶斯估计和信度估计,并证明了这些估计的强相合性.在均方误差的意义下比较了这些估计的好坏,并通过数值模拟对均方误差进行了验证,结果表明,贝叶斯估计比其他估计具有较小的均方误差.最后,给出了结构参数的估计并证明了经验贝叶斯估计和经验贝叶斯信度估计的渐近最优性.     

基于VaR和ES调整的Sharpe比率及在基金评价中的实证研究

传统Sharpe比率将投资收益的标准差作为风险的度量,而实证研究中更关注基金的损失风险而非全部风险,这是收益标准差所无法准确刻画的。针对传统Sharpe比率的这一缺点,本文考虑了用于度量下方风险的指标风险价值VaR(Value at Risk)和预期不足ES(Expected Shortfall)来替代投资收益的标准差,从而对传统Sharpe比率进行了调整。这里对VaR和ES进行计算时,运用了经验非参数估计和非参数平滑核估计两种方法。此外,本文还考虑了基金收益随时间波动的动态性,用广义自回归异方差GARCH模型对收益波动进行模拟,考察动态的VaR和ES,在实践中以动态的VaR和ES评价风险收益更加灵活。在实证研究中,本文用传统的Sharpe比率、基于VaR和ES的Sharpe比率以及基于条件VaR和条件ES的条件Sharpe比率对国内证券市场上所有26只封闭式基金在2005-2009年间的业绩进行了实证分析,分析了基金在不同指标下所体现的风险控制能力和收益水平的差别,并基于不同指标对所有基金进行了排名。此外,本文还运用协整检验考察基金收益率与市场基准指数是否存在联动关系,检验证明两者并不存在长期的均衡关系。     

Estimating Value-at-Risk and Expected Shortfall using the intraday low and range data

Value-at-Risk (VaR) is a popular measure of market risk. To convey information regarding potential exceedances beyond the VaR, Expected Shortfall (ES) has become the risk measure for trading book bank regulation. However, the estimation of VaR and ES is challenging, as it requires the estimation of the tail behaviour of daily returns. In this paper, we take advantage of recent research that develops joint scoring functions for VaR and ES. Using these functions, we present a novel approach to estimating the two risk measures based on intraday data. We focus on the intraday range, which is the difference between the highest and lowest intraday log prices. In contrast to intraday observations, the intraday low and high are widely available for many financial assets. To alleviate the challenge of modelling extreme risk measures, we propose the use of the intraday low series. We draw on a theoretical result for Brownian motion to show that a quantile of the daily returns can be estimated as the product of a constant term and a less extreme quantile of the intraday low returns, which we define as the difference between the lowest log price of the day and the log closing price of the previous day. In view of this, we use estimates of the VaR and ES of the intraday low returns to estimate the VaR and ES of the daily returns. We provide empirical support for the new proposals using data for five stock indices and five individual stocks.     

Bayesian approaches for analyzing earthquake catastrophic risk

Extreme value theory has been widely used in analyzing catastrophic risk. The theory mentioned that the generalized Pareto distribution (GPD) could be used to estimate the limiting distribution of the excess value over a certain threshold; thus the tail behaviors are analyzed. However, the central behavior is important because it may affect the estimation of model parameters in GPD, and the evaluation of catastrophic insurance premiums also depends on the central behavior. This paper proposes four mixture models to model earthquake catastrophic loss and proposes Bayesian approaches to estimate the unknown parameters and the threshold in these mixture models. MCMC methods are used to calculate the Bayesian estimates of model parameters, and deviance information criterion values are obtained for model comparison. The earthquake loss of Yunnan province is analyzed to illustrate the proposed methods. Results show that the estimation of the threshold and the shape and scale of GPD are quite different. Value-at-risk and expected shortfall for the proposed mixture models are calculated under different confidence levels.     

Evaluating Currency Risk in Emerging Markets

We present a systematic approach to the problem of evaluating currency risk. The approach involves a test for stationarity, and a method of estimating Value-at-Risk (VaR) and Expected Shortfall (ES) from dependent heavy-tailed data. Various estimation methods are compared and the accuracy of the approach is discussed. An application of the technique to the Mexican peso/US dollar exchange rate reveals the level of currency risk foreign investors face in Mexico.      

计算资产组合市场风险值的一种有效方法

市场风险值(VaR)是一种常用的度量风险的方法．本文采用极值理论中的阈值模型来计算VaR．基于中国上证指数和深成指数的收盘价，构造超越阈值的极值渐近概率分布，所得到的计算结果与传统方法相比较，有明显的优越性和更好的精度．     

A New Robust Risk Measure: Quantile Shortfall

Among recent measures for risk management, value at risk (VaR) has been criticized because it is not coherent and expected shortfall (ES) has been criticized because it is not robust to outliers. Recently,[Math. Oper. Res., 38, 393-417 (2013)] proposed a risk measure called median shortfall (MS) which is distributional robust and easy to implement. In this paper, we propose a more generalized risk measure called quantile shortfall (QS) which includes MS as a special case. QS measures the conditional quantile loss of the tail risk and inherits the merits of MS. We construct an estimator of the QS and establish the asymptotic normality behavior of the estimator. Our simulation shows that the newly proposed measures compare favorably in robustness with other widely used measures such as ES and VaR.     

t-分布与不同风险度量下有效投资组合及其边缘的相互关系研究

In order to study the effect of different risk measures on the efficient portfolios (frontier) while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivariate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios (frontier) based on risk measures such as variance, value at risk (VaR), and expected shortfall (ES) is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance (MV) efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.     

STUDY ON THE INTERRELATION OF EFFICIENT PORTFOLIOS AND THEIR FRONTIER UNDER t DISTRIBUTION AND VARIOUS RISK MEASURES

In order to study the effect of different risk measures on the efficient portfolios (frontier) while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivari-ate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios (frontier) based on risk measures such as variance, value at risk (VaR), and expected shortfall (ES) is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance (MV) efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.     

GDP分布模型与股票收益率的极值分析

本文讨论了利用 GDP分布模型计算 Va R和 ES的方法 ,并利用此模型对 FT 3 0指数进行了实证分析 ,得到了满意的 Va R和 ES估计值 .     

STUDY ON THE INTERRELATION OF EFFICIENT PORTFOLIOS AND THEIR FRONTIER UNDER t DISTRIBUTION AND VARIOUS RISK MEASUREgS

In order to study the effect of different risk measures on the efficient portfolios （fron- tier） while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivariate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios （frontier） based on risk measures such as variance, value at risk （VaR）, and expected shortfall （ES） is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance （MV） efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.