Portfolio value-at-risk estimation in energy futures markets with time-varying copula-GARCH model

This paper combines copula functions with GARCH-type models to construct the conditional joint distribution, which is used to estimate Value-at-Risk (VaR) of an equally weighted portfolio comprising crude oil futures and natural gas futures in energy market. Both constant and time-varying copulas are applied to fit the dependence structure of the two assets returns. The findings show that the constant Student t copula is a good compromise for effectively fitting the dependence structure between crude oil futures and natural gas futures. Moreover, the skewed Student t distribution has a better fit than Normal and Student t distribution to the marginal distribution of each asset. Asymmetries and excess kurtosis are found in marginal distributions as well as in dependence. We estimate VaR of the underlying portfolio to be 95% and 99%, by using the Monte Carlo simulation. Then using backtesting, we compare the out-of-sample forecasting performances of VaR estimated by different models.     

Estimating and forecasting portfolio’s Value-at-Risk with wavelet-based extreme value theory: Evidence from crude oil prices and US exchange rates

This article proposes a wavelet-based extreme value theory (W-EVT) approach to estimate and forecast portfolio’s Value-at-Risk (VaR) given the stylized facts and complex structure of financial data. Our empirical application to portfolios of crude oil prices and US dollar exchange rates shows that the W-EVT models provide an effective and powerful tool for gauging extreme moments and improving the accuracy of portfolio’s VaR estimates and forecasts after noise is removed from the original data.     

极值理论在风险度量中的应用--基于上证180指数

精确度量风险是金融风险管理的关键问题。本引入广义帕雷托分布代替传统的正态分布等，精确描述金融收益的厚尾特征。并将基于广义帕雷托分布的VaR模型和其它模型方法，如GARCH(1，1)、GARCH(1，1)-t、历史模拟法、方差-协方差方法，进行比较分析。实证研究表明，基于广义帕雷托分布的VaR模型比传统的模型方法更适合厚尾分布高分位点的预测，并且其预测结果比较稳定。这使得基于广义帕雷托分布的VaR模型成为VaR度量方法中最稳健的方法之一。     

不同市态下正态性转换时变VaR

VaR技术作为全球广为流行的金融风险管理技术,其测度的是极端情况下的风险头寸,但在传统假设下可能会极大地低估其值,这就会使得在实践中使用VaR值作为风险管理标准时面临更大的新的风险.考虑我国股市处于不同市场态势下对风险头寸的影响,就牛、熊市中分别估测VaR值.首先利用各种Delta-Gamma-Johnson转换函数对经验数据进行正态性调整.考虑通过转换机制调整后的经验数据仍然存在的异方差性特征,然后运用GARCH模型计算时变VaR值,以此来改善VaR的计算风险,探讨我国股票市场VaR技术的适用性和准确性.     

风险值的估计及其周期分析

本文提出了两种风险值的估计方法，这两种方法均是先估计出收益的分布，然后求得分布左侧p分位点作为风险值的估计．第一种方法是用核估计方法得到收益的分布估计；第二种方法则是由分布的核估计算得收益的众数，引入所谓的广义半t分布拟合众数左侧的样本．文章以上证指数为实例验证了这两种方法的可行性与精确性．最后我们利用上述两种估计方法得到了上证指数风险值的波动主周期．     

一类重尾风险因子的模拟及其投资高风险值和置信区间的估计

由于金融市场中的日周期或短周期对数回报率的样本数据多数呈现胖尾分布，于是现有的正态或对数正态分布模型都在不同程度上失效，为了准确模拟这种胖尾分布和提高投资风险估计及金融管理，本文引进了一种可根据实际金融市场数据作出调正的蒙特卡洛模拟方法．这个方法可以有效地复制金融产品价格的日周期对数回报率数据的胖尾分布．结合非参数估计方法，利用该模拟方法还得到投资高风险值以及高风险置信区间的准确估计。     

极值理论在高频数据中的VaR和CVaR风险价值研究

高频数据具有与低频数据明显不同的特征。本文引入广义帕雷托分布代替传统的正态分布等,精确描述金融高频数据收益的厚尾特征;并且计算高频数据下的VaR和CVaR,然后利用深成A指数据进行返回检验。两种返回检验方法的结果表明,极值理论方法可以比较精确地度量VaR和CVaR。     

Bias correction in extreme value statistics with index around zero

Applying extreme value statistics in meteorology and environmental science requires accurate estimators on extreme value indices that can be around zero. Without having prior knowledge on the sign of the extreme value indices, the probability weighted moment (PWM) estimator is a favorable candidate. As most other estimators on the extreme value index, the PWM estimator bears an asymptotic bias. In this paper, we develop a bias correction procedure for the PWM estimator. Moreover, we provide bias-corrected PWM estimators for high quantiles and, when the extreme value index is negative, the endpoint of a distribution. The choice of k, the number of high order statistics used for estimation, is crucial in applications. The asymptotically unbiased PWM estimators allows the choice of higher level k, which results in a lower asymptotic variance. Moreover, since the bias-corrected PWM estimators can be applied for a wider range of k compared to the original PWM estimator, one gets more flexibility in choosing k for finite sample applications. All advantages become apparent in simulations and an environmental application on estimating “once per 10,000 years” still water level at Hoek van Holland, The Netherlands.     

我国股市收益的双长记忆性检验——基于VaR估计的ARFIMA-HYGARcH-skt模型

针对股市收益分布的"尖峰肥尾"特征,引入了偏t分布作为新息分布。基于VaR方法,从风险估计的角度,利用ARFIMA(2,d_1,0)-HYGARCH(1,d_2,1)-skt模型对1996年12月17日至2007年7月5日期间的沪深股市收益进行了实证分析.实证结果显示:沪深股市具有显著的双长记忆特征;上海股市的日收益率和波动率的长记忆性均比深圳股市强;ARFIMA(2,d_1,0)- HYGARCH(1,d_2,1)-skt模型对我国股市收益具有较强的风险估计和预测能力。     

基于GAS模型的动态VaR预测效果分析

GAS模型是一种基于观测的动态模型,理论简单且应用灵活,可以直接估计VaR.将GAS模型和GARCH类模型应用于不同条件下生成的模拟数据和三个时间段的沪深300指数的日对数收益率数据,并比较模型关于VaR的预测效果。结果表明:在对称的条件分布下,GAS模型容易高估风险且不稳健,其表现不如GARCH类模型;但在条件分布为有偏的时,GAS模型与GARCH类模型的表现相当,部分情况下会优于GARCH类模型,尤其在实证分析中关于序列2和序列3的VaR的估计,GAS模型的预测效果较好。因此,实际应用中,对于具有较明显偏态分布或尖峰分布的数据可以考虑使用GAS模型预测动态VaR.     

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 method for estimating the forecast quality with consideration for the errors of calculating the unknown parameters

In this study, the problem of estimating the forecast accuracy of a model is considered. A widespread practice is to approximate the population expectation of the forecast accuracy by the sample expectation, which is equivalent to the uniform consideration for the deviations of the forecast from the exact value of a quantity for all time moments. If the vector of unknown parameters is estimated at each step only from the preceding observations, the significance of the deviations is not the same at all time moments. In this study, we propose a method that takes into account the forecast errors with different weights. The problem of constructing the most accurate estimate of the forecast quality, a parameter from which the condition for the optimal weights can be derived, is formalized. Monte-Carlo experiments are used to compare the accuracy of the methods for estimating the forecast quality in the cases when the observations are taken into account with the same weights, with optimum weights, and with the weights calculated using a numerical procedure.     

Estimation of Value at Risk by Extreme Value Methods

Value at Risk (VaR) is defined as a low quantile in the distribution of financial profits and losses. It is the most commonly used measure of market risk in the financial industry. The methods currently used for estimation of VaR have various short comings as they are not aimed specifically at modeling the tails of the distribution of profits and losses; extreme value methods may prove valuable towards improving the current estimation methods. In this paper we give an overview of the current state of the art in applying extreme value methods to financial data and the problems encountered when doing so. We compare the performance of methods currently used for estimation of VaR to the performance of various extreme value methods and outline advantages and drawbacks of the different methods.     

核密度估计在预测风险价值中的应用

通过研究核密度估计理论,提出了一种适应估计金融时间序列分布的L ap lace核密度函数.在单变量核密度估计的基础上建立了风险价值(V a lua at R isk,简记为VaR)预测的预测模型.通过对核密度估计变异系数的加权处理建立了两种加权VaR预测模型.最后,通过上证指数收益率对建立的VaR预测模型进行了实证分析,结果显示两种加权方法对上证指数收益率的VaR预测具有较高的效率.     

基于Copula的VsR度量与事后检验

估计VaR的传统方法有三种:协方差矩阵法、历史模拟法和蒙特仁洛模拟法。通常,文献中认为刚蒙特卡洛模拟法度量VaR有很多方面的优点。但是,本文通过实证检验发现,使用传统蒙特卡洛模拟法估计的VaR偏小,事后检验效果很不理想。本文引入Copula函数来改进传统的蒙特卡洛模拟法。Copula函数能将单个边际分布和多元联合分布联系起来,能处理非正态的边际分布,并且它度量的相关性不再局限于线性相关性。实证检验表明,基于Copula的蒙特卡罗模拟法可以更加准确地度量资产组合的VaR。     

基于GARCH族模型的沪深300股指VaR度量

本文在修正了沪深300股票指数收益率序列的非平稳性和自身相关性之后,把ARMA模型与GARCH模型、GJR模型、IGARCH模型、FIGARCH模型、FIEGARCH模型、FIAPARCH模型、HYGARCH模型相结合,然后依次假设残差分布服从正态分布、t分布和偏t分布,来描述沪深300股票指数日对数收益率序列的尖峰厚尾性、杠杆效应和长记忆特性,利用上述模型分别计算沪深300股票指数的VaR值.在空头和多头投资者情况下,不同的波动性模型和不同残差分布的VaR预测有效性差距很大.比较得知,在不同的置信水平下,沪深300股票指数收益率序列空头和多头的VaR预测成功概率比较高的模型有HYGARCH和FIEGARCH这两类具有长记忆性的模型.     

基于Copula的供应链金融质物组合价格风险测度研究

本文选取白银、铝和铜三种供应链金融质物作为研究对象,在分析三种质物收益率统计特征的基础上,引入Copula模型刻画供应链金融业务中质物收益率的“尖峰厚尾”特征以及质物收益率之间的非线性相关结构;采用Monte Carlo模拟方法测度考虑到极端情况下的质物组合价格风险值CVaR;利用时间平方根法则测度长周期视角下质物组合的价格风险。将CVaR与VaR测度结果进行对比,比较分析短期价格风险与长期价格风险,将Copula模型与传统风险测度方法下计算出的风险值进行对比,以期选取最优测度供应链金融质物组合长期价格风险模型。研究结果表明:从单一质物价格波动特征来看,三种单一质物的收益率均存在非正态分布和“尖峰厚尾”特征,具有一般金融资产收益率分布的特点。从模型的有效性来看,第一,CVaR比VaR能够更好地、全面地测度供应链金融质物组合的价格风险;第二,基于Copula模型的风险测度结果比传统集成风险测度结果的准确性高;第三,平方欧式距离法结果表明在五种Copula模型中,t-Copula是最优刻画供应链金融质物组合收益率间的相依关系的模型。从长短期风险测度结果来看,随着风险期限的增加,质物组合的价格风险值随之增大,以往研究中用短期风险测度往往会低估商业银行所面临的价格风险,不利于商业银行资金信贷的优化配置。得到的结论对我国商业银行开展供应链金融业务防范价格风险提供了量化支持。     

Denoising deep extreme learning machine for sparse representation

In recent years, a great deal of research has focused on the sparse representation for signal. Particularly, a dictionary learning algorithm, K-SVD, is introduced to efficiently learn an redundant dictionary from a set of training signals. Indeed, much progress has been made in different aspects. In addition, there is an interesting technique named extreme learning machine (ELM), which is an single-layer feed-forward neural networks (SLFNs) with a fast learning speed, good generalization and universal classification capability. In this paper, we propose an optimization method about K-SVD, which is an denoising deep extreme learning machines based on autoencoder (DDELM-AE) for sparse representation. In other words, we gain a new learned representation through the DDELM-AE and as the new “input”, it makes the conventional K-SVD algorithm perform better. To verify the classification performance of the new method, we conduct extensive experiments on real-world data sets. The performance of the deep models (i.e., Stacked Autoencoder) is comparable. The experimental results indicate the fact that our proposed method is very efficient in the sight of speed and accuracy.     

Estimating value at risk of portfolio by conditional copula-GARCH method

Copula functions represent a methodology that describes the dependence structure of a multi-dimension random variable and has become one of the most significant new tools to handle risk factors in finance, such as Value-at Risk (VaR), which is probably the most widely used risk measure in financial institutions. Combining copula and the forecast function of the GARCH model, this paper proposes a new method, called conditional copula-GARCH, to compute the VaR of portfolios. This work presents an application of the copula-GARCH model in the estimation of a portfolio’s VaR, composed of NASDAQ and TAIEX. The empirical results show that, compared with traditional methods, the copula model captures the VaR more successfully. In addition, the Student-t copula describes the dependence structure of the portfolio return series quite well.     

Estimating allocations for Value-at-Risk portfolio optimization

Value-at-Risk, despite being adopted as the standard risk measure in finance, suffers severe objections from a practical point of view, due to a lack of convexity, and since it does not reward diversification (which is an essential feature in portfolio optimization). Furthermore, it is also known as having poor behavior in risk estimation (which has been justified to impose the use of parametric models, but which induces then model errors). The aim of this paper is to chose in favor or against the use of VaR but to add some more information to this discussion, especially from the estimation point of view. Here we propose a simple method not only to estimate the optimal allocation based on a Value-at-Risk minimization constraint, but also to derive—empirical—confidence intervals based on the fact that the underlying distribution is unknown, and can be estimated based on past observations.