基于Expectile风险建模的原油价格风险测度研究

以西德克萨斯中质原油(WTI)为研究对象,采用expectile模型测度原油价格风险,同时引入极值理论,构建exepctile-EVT模型刻画极端风险。研究表明:油价收益序列具有典型的长记忆性和自相关特征;油价的涨跌会影响多头风险,而空头风险仅受油价下跌的影响;引入极值理论后的expectile-EVT模型能很好地刻画极端风险的动态演化规律,其预测结果也比其他模型更合理。     

多元极值的参数建模方法及其金融应用：最新进展述评

 由于现实中的极值事件往往倾向于同时或相继发生,因此多元极值研究正成为极值统计学的理论前沿和研究热点。本文对该领域中参数建模方法的最新进展做了系统性述评,包括经典多元极值理论、Ledford-Tawn-Ramos方法和Heffernan和Tawn条件法等,并指出了这些建模方法的优缺点以及未来可能的理论突破点。本文还全面分析了近年来多元极值分析方法在金融领域的国内外应用现状,并探讨其未来的应用前景,可能是在金融传染、组合问题和系统性风险管理等方面。     

极值理论在巨灾损失拟合中的应用

极值理论是一种研究极值事件统计规律的方法,文章利用我国火灾历年损失额的数据建立了极值模型.我们发现,利用传统方法描述火灾损失额的统计规律会忽略极值数据的存在,但结合极值分布的建模效果要明显好于传统方法.     

二项—Gumbel复合极值分布的参数估计

在金融风险评估、事故预测、保险索赔等领域的研究中,极值理论已发展成为一种重要的统计学方法.Gumbel分布是一种常用的极值分布函数,并逐渐成为了对于随机变量极端变异性建模的重要工具.文章将二项分布与Gumbel分布函数复合,提出了一种新的复合极值分布函数即二项-Gumbel分布.重点介绍了极值理论以及二项分布与Gumbel分布复合函数,运用极大似然估计(MLE)对二项-Gumbel复合分布的各种参数进行估计,并通过计算机模拟得KS检验统计量的临界值.     

平稳序列的GPD模型在风险测度中的应用

文章旨在运用极值理论提高VaR的适用性和估计的精确度.VaR技术作为一种统计方法常用来测度金融市场风险,极值理论则是研究随机变量或过程的极端情形的统计规律性.然而,经典的极值模型要求金融时序服从独立同分布条件.考虑满足平稳性条件下的金融时序,针对序列相关引致的极值成串现象,引入极值指标来刻画极值数据间的相关结构,采用除串技术过滤数据的相关性,进而得到渐进独立的同分布序列,再构建GPD模型来测度VaR.实证分析和回测检验表明:改进的GPD阈值模型具有对风险测度的有效性和精确性.     

极值理论在VaR中的运用

极值理论(extreme value theory)是次序统计理论的一个分支,将统计学中的极值理论用于VaR的计算,是一种崭新的方法.1987年10月发生的美国股票市场崩盘,1992年9月欧洲货币体系的瓦解和1997年开始的亚洲金融危机都是金融业和风险管理中的中心议题,如何处理像这样的极端事件在风险管理中极其重要.     

BMM模型在商业银行操作风险度量中的应用

文章利用极值理论中的BMM模型对商业银行操作风险损失极端值分布进行估计,采用广义极值分布构建VaR模型,组建极值数据组,运用极大似然估计法估计两个参数,进而计算操作风险损失VaR。最后结合我国商业银行1994~2008年的220个操作风险损失数据进行实证研究,结果显示BMM模型具有超越样本的估计能力,在数据较少条件下能得到较准确结果,用其度量商业银行的操作风险损失VaR是合理的,这为我国商业银行操作风险度量和管理提供一定的量化依据。     

基于POT-GPD损失分布的农业自然灾害VAR估算

 近年来,干旱、洪涝、雪灾等极端气象灾害频发,强烈冲击农业生产和粮食安全,科学估算农业自然灾害给粮食产出带来的风险价值,对预警农业自然灾害、确保粮食安全具有重要意义。文章针对农业自然灾害大灾损失的低频高损、数据稀少的特点,采用极值理论中的POT 模型对历史观测值超阀值数据进行建模,运用GPD模型对农业自然大灾损失进行拟合,模拟计算农业自然灾害VAR值,为农业自然灾害预警和粮食安全储备提供科学依据。     

极值Copula在商业银行操作风险度量中的应用

本文主要内容是针对新巴塞尔协议把商业银行操作风险纳入风险量化和监管领域,应用极值Copula函数分析我国商业银行各类操作风险之间的相依结构,将操作风险度量从一维拓展到多维。目前对所有的事件类型值简单加总求得操作风险的总资本要求,没有考虑事件类型之间的相关性,这与实际情况是不符合的。为此本文在分析我国商业银行各类操作风险之间的相依性的基础上,运用极值Copula函数建立实际操作风险的相依结构,构建计算操作风险总VaR值的极值Copula模型。     

CVaR-EVT和BMM在极端金融风险管理中的应用研究

随着风险度量一致性原则的提出,研究发现金融机构广泛采用的VaR模型存在严重不足,尤其针对分布具有厚尾特征的极端金融风险无法有效度量。本文采用极值理论（EVT）解决VaR方法的尾部度量不足问题,利用CVaR-EVT和BMM模型分析美国、香港股票市场和我国沪深两市指数18年的日收益数据,研究发现：（1）在95％置信区间及点估计中,分位数为99%的CVaR-EVT所揭示的极端风险优于VaR的估计值;且BMM方法为实施长期极端风险管理提供了有力决策依据,其回报率受分段时区的影响,期间越长,风险估计值越高;（2）模型采用ML和BS方法统计估值显示,我国股票市场极端风险尾部估计值高于香港和美国市场;但是,国内市场逐步稳定,并呈现出跟进国际市场且差距缩小的发展趋势。     

POT模型在巨灾损失预测中的应用——基于MCMC方法的估计

极值统计学主要研究随机事件极端情况的统计规律性。运用POT模型拟合中国暴雨损失数据,确定损失超出量的分布形式。实证分析表明,借助POT模型对巨灾风险损失分布进行估计是较为合理的,但当数据量较小时,使用基于Gibbs抽样的MCMC方法估计POT模型的参数,可以解决样本数据不足导致的极大似然估计中误差增大的问题。     

Geoadditive modeling for extreme rainfall data

Extreme value models and techniques are widely applied in environmental studies to define protection systems against the effects of extreme levels of environmental processes. Regarding the matter related to the climate science, a certain importance is covered by the implication of changes in the hydrological cycle. Among all hydrologic processes, rainfall is a very important variable as it is strongly related to flood risk assessment and mitigation, as well as to water resources availability and drought identification. We implement here a geoadditive model for extremes assuming that the observations follow a generalized extreme value distribution with spatially dependent location. The analyzed territory is the catchment area of the Arno River in Tuscany in Central Italy.     

A Bayesian approach to zero-inflated data in extremes

Abstract

The generalized extreme value (GEV) distribution is known as the limiting result for the modeling of maxima blocks of size n, which is used in the modeling of extreme events. However, it is possible for the data to present an excessive number of zeros when dealing with extreme data, making it difficult to analyze and estimate these events by using the usual GEV distribution. The Zero-Inflated Distribution (ZID) is widely known in literature for modeling data with inflated zeros, where the inflator parameter w is inserted. The present work aims to create a new approach to analyze zero-inflated extreme values, that will be applied in data of monthly maximum precipitation, that can occur during months where there was no precipitation, being these computed as zero. An inference was made on the Bayesian paradigm, and the parameter estimation was made by numerical approximations of the posterior distribution using Markov Chain Monte Carlo (MCMC) methods. Time series of some cities in the northeastern region of Brazil were analyzed, some of them with predominance of non-rainy months. The results of these applications showed the need to use this approach to obtain more accurate and with better adjustment measures results when compared to the standard distribution of extreme value analysis.     

Scoring predictions at extreme quantiles

AStA Advances in Statistical Analysis - Prediction of quantiles at extreme tails is of interest in numerous applications. Extreme value modelling provides various competing predictors for this...     

Using copulas for rating weather index insurance contracts

This study develops a methodology for a copula-based weather index insurance design. Because the copula approach is better suited for modeling tail dependence than the standard linear correlation approach, its use may increase the effectiveness of weather insurance contracts designed to provide protection against extreme weather events. In our study, we employ three selected Archimedean copulas to capture the left-tail dependence in the joint distribution of the farm yield and a specific weather index. A hierarchical Bayesian model is applied to obtain consistent estimates of tail dependence using relatively short time series. Our empirical results for 47 large grain-producing farms from Kazakhstan indicate that, given the choice of an appropriate weather index to signal catastrophic events, such as a severe drought, copula-based weather insurance contracts may provide significantly higher risk reductions than regression-based indemnification schemes.     

Spatial modeling of extreme rainfall in northeast Thailand

It is well recognized that the generalized extreme value (GEV) distribution is widely used for any extreme events. This notion is based on the study of discrete choice behavior; however, there is a limit for predicting the distribution at ungauged sites. Hence, there have been studies on spatial dependence within extreme events in continuous space using recorded observations. We model the annual maximum daily rainfall data consisting of 25 locations for the period from 1982 to 2013. The spatial GEV model that is established under observations is assumed to be mutually independent because there is no spatial dependency between the stations. Furthermore, we divide the region into two regions for a better model fit and identify the best model for each region. We show that the regional spatial GEV model reflects the spatial pattern well compared with the spatial GEV model over the entire region as the local GEV distribution. The advantage of spatial extreme modeling is that more robust return levels and some indices of extreme rainfall can be obtained for observed stations as well as for locations without observed data. Thus, the model helps to determine the effects and assessment of vulnerability due to heavy rainfall in northeast Thailand.     

Non-parametric Estimation of Tail Dependence

Abstract.  Dependencies between extreme events (extremal dependencies) are attracting an increasing attention in modern risk management. In practice, the concept of tail dependence represents the current standard to describe the amount of extremal dependence. In theory, multi-variate extreme-value theory turns out to be the natural choice to model the latter dependencies. The present paper embeds tail dependence into the concept of tail copulae which describes the dependence structure in the tail of multivariate distributions but works more generally. Various non-parametric estimators for tail copulae and tail dependence are discussed, and weak convergence, asymptotic normality, and strong consistency of these estimators are shown by means of a functional delta method. Further, weak convergence of a general upper-order rank-statistics for extreme events is investigated and the relationship to tail dependence is provided. A simulation study compares the introduced estimators and two financial data sets were analysed by our methods.