基于EGB2分布族的GAS-EGARCH模型与VaR预测

GARCH族模型是刻画资产收益率的常用工具,在风险度量领域具有广泛应用。为了更有效地描述收益率的偏斜厚尾等特征,越来越多学者对GARCH族模型的条件分布形式进行了研究。但是仅对GARCH模型条件分布进行修正是不够的,还需要对模型本身的函数形式进行修正。基于得分函数的时变参数建模思想近年来受到广泛关注,本文借助这一思想对EGARCH模型中对数标准差进行时变波动建模,并利用EGB2分布族作为模型的条件分布,进而建立GAS-EGARCH-EGB2模型。以我国10只中证行业指数为研究对象考察GAS-EGARCH-EGB2模型的风险预测效果,GAS-EGARCH-EGB2模型样本外VaR预测表现普遍优于ACM-EGARCH-EGB2模型。     

Modeling fat tails in stock returns: a multivariate stable-GARCH approach

In this paper a new multivariate volatility model is proposed. It combines the appealing properties of the stable Paretian distribution to model the heavy tails with the GARCH model to capture the volatility clustering. Returns on assets are assumed to follow a sub-Gaussian distribution, which is a particular multivariate stable distribution. In this way the characteristic function of the fitted returns has a tractable expression and the density function can be recovered by numerical methods. A multivariate GARCH structure is then adopted to model the covariance matrix of the Gaussian vectors underlying the sub-Gaussian system. The model is applied to a bivariate series of daily U.S. stock returns. Value-at-risk for long and short positions is computed and compared with the one obtained using the multivariate normal and the multivariate Student’s t distribution. Finally, exploiting the recent developments in the vast dimensional time-varying covariances modeling, possible feasible extensions of our model to higher dimensions are suggested and an illustrative example using the Dow Jones index components is presented.     

RCA models with correlated errors

Financial time series data cannot be adequately modelled by a normal distribution and empirical evidence on the non-normality assumption is very well documented in the financial literature; see [R.F. Engle, Autoregressive conditional heteroskedasticity with estimates of the variance of UK inflation, Econometrica 50 (1982) 987–1008] and [T. Bollerslev, Generalized autoregressive conditional heteroscedasticity, J. Econometrics 31 (1986) 307–327] for details. The kurtosis of various classes of RCA models has been the subject of a study by Appadoo et al. [S.S. Appadoo, M. Gharahmani, A. Thavaneswaran, Moment properties of some volatility models, Math. Sci. 30 (2005) 50–63] and Thavaneswaran et al. [A. Thavaneswaran, S.S. Appadoo, M. Samanta, Random coefficient GARCH models, Math. Comput. Modelling 41 (2005) 723–733]. In this work we derive the kurtosis of the correlated RCA model as well as the normal GARCH model under the assumption that the errors are correlated.     

基于价格极差的GARCH模型

本文利用资产价格的极差序列,基于常规GARCH模型的框架,构造了一类关于波动率的新模型,即GARCH-R模型以及能够表达波动率变化非对称性特性的AGARCH-R模型。利用上证综合指数日收益率及相应的高频数据,通过比较不同模型对波动率以及VAR的预测效果,揭示了这种包含了极差信息的新的模型比传统的GARCH类模型的预测效果具有显著的优势。     

A conditional-SGT-VaR approach with alternative GARCH models

This paper proposes a conditional technique for the estimation of VaR and expected shortfall measures based on the skewed generalized t (SGT) distribution. The estimation of the conditional mean and conditional variance of returns is based on ten popular variations of the GARCH model. The results indicate that the TS-GARCH and EGARCH models have the best overall performance. The remaining GARCH specifications, except in a few cases, produce acceptable results. An unconditional SGT-VaR performs well on an in-sample evaluation and fails the tests on an out-of-sample evaluation. The latter indicates the need to incorporate time-varying mean and volatility estimates in the computation of VaR and expected shortfall measures.     

基于Skewed-t分布的FIGARCH模型与VaR的度量

金融资产收益率序列的波动具有典型的尖峰厚尾和非对称性特征,描述这种特性需以合适的概率分布函数为基础.因此,寻求更好的概率分布函数对风险度量、VaR的计算有着十分重要的意义.有鉴于此引入Skewed-t分布度量VaR,并比较分析了RiskMetrics及FIGARCH类模型度量VaR值的准确程度,本文同时分析了多头头寸和空头头寸情况下的VaR.结果表明,在两种头寸情况下,Skewed-t分布在空头和多头情形对资产厚尾特性以及非对称性的拟合效果均要比正态分布好;在两种头寸中不同的置信水平下,FIAGARCH(CHUNG)模型预测的VaR值改进了使用传统模型的精确性,高估或低估风险的程度较轻.     

基于ARFIMA-HYGARCH-M-VaR模型的亚洲汇率市场均值和波动过程的双长期记忆性测度研究

作为金融传导机制的一个重要成分,汇率在金融危机的传播中发挥着重要作用.因此本文以亚洲汇率市场的汇率作为研究样本,通过引入skt分布来刻画残差的分布,构建了ARFIMA-HYGARCH-M-VaR模型来测度汇率风险值,并与skt分布下的GARCH及FIGARCH模型的VaR进行失败率回测检验与动态分位数测试.研究结果表明:在不同显著性水平下,skt分布下的各种模型基本都有较好的风险测度能力,且ARFIMA-HYGARCH-M模型的VaR风险测度更加精确与稳定.本研究为我国及亚洲其他国家汇率市场的风险测度与风险管理提供了一定的理论借鉴和方法基础.     

RCA model with quadratic GARCH innovation distribution

Rapid development of time series models addressing volatility has recently been reported in the financial literature. Often the standardized residuals from an RCA (Random coefficient autoregressive) model still has fat tails, thus suggesting using a fat-tailed error distribution instead. Kurtosis of GARCH model plays an important role in option pricing applications with real data. This paper considers some volatility models with quadratic GARCH innovations and derive the kurtosis of the process.     

A GARCH option pricing model with α-stable innovations

We develop an option pricing model which is based on a GARCH asset return process with α-stable innovations with truncated tails. The approach utilizes a canonic martingale measure as pricing measure which provides the possibility of a model calibration to market prices. The GARCH-stable option pricing model allows the explanation of some well-known anomalies in empirical data as volatility clustering and heavy tailedness of the return distribution. Finally, the results of Monte Carlo simulations concerning the option price and the implied volatility with respect to different strike and maturity levels are presented.     

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。     

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.     

Improving density forecast by modeling asymmetric features: An application to S&P500 returns

A density forecast is an estimate of the probability distribution of the possible future values of a random variable. From the current literature, an economic time series may have three types of asymmetry: asymmetry in unconditional distribution, asymmetry in conditional distribution, volatility asymmetry. In this paper, we propose three density forecasting methods under two-piece normal assumption to capture these asymmetric features. A GARCH model with two-piece normal distribution is developed to capture asymmetries in the conditional distributions. In this approach, we first estimate parameters of a GARCH model by assuming normal innovations, and then fit a two-piece normal distribution to the empirical residuals. Block bootstrap procedure, and moving average method with two-piece normal distribution are presented for volatility asymmetry and asymmetry in the conditional distributions. Application of the developed methods to the weekly S&P500 returns illustrates that forecast quality can be significantly improved by modeling these asymmetric features.     

向量GARCH族模型计算中国金融市场投资组合风险价值(VaR)的比较研究与评述

对由上证综合指数、深证成分指数、上证基金指数、上证国债指数计算的日自然对数收益率组成的数据矩阵,分别建立了残差服从正态分布、t分布的向量ARCH、向量GARCH、纯对角GARCH、BEKK、常条件相关GARCH、主成分GARCH和EWMA模型,基于这些模型,计算了风险价值(VaR),进而通过比较计算结果,得出BEKK—t模型测算中国金融市场投资组合的风险价值(VaR)效果最好等的结论.     

NGARCH模型在证券投资风险分析中的应用

应用NGARCH模型在三种分布假设下对上证综合指数进行了V aR风险值估计,并且与GARCH模型和APARCH模型估计结果作比较,通过返回检验,发现NGARCH模型应用于V aR估计是统计有效的,且优于GARCH和APARCH模型.     

两类多元GARCH模型的预测绩效和组合VaR的研究

运用V aR模型对股票组合进行风险测度的关键之一是得到组合条件协方差矩阵.而经典的多元GARCH模型来求解波动率面临着估计参数过多,计算量庞大的问题.因此,使用正交GARCH模型和CCC模型来估算波动率,并以沪深两市A股市场上四个行业的65只股票为样本,使用RM SE和M AD指标比较这些模型的预测能力,求得股票组合的V aR,得出前者效率高和后者预测能力略高的结论.     

基于时变Copula模型的 基金收益率相依关系的应用研究

基于时变Copula模型,获得预测方差,确定单个基金收益率序列的边缘分布.利用常见的静态Copula和时变Copula模型对基金收益率序列间两两相依关系进行建模并进行对比分析.应用研究表明,基于MCMC方法的时变Copula模型能更有效地度量基金收益率序列的风险.     

基于动态VaR约束与随机波动率模型的最优投资策略

研究Stein-Stein随机波动率模型下带动态VaR约束的最优投资组合选择问题. 假设投资者的目标是最大化终端财富的期望幂效用,可投资于无风险资产和一种风险资产, 风险资产的价格过程由Stein-Stein随机波动率模型刻画. 同时, 投资者期望能在投资过程中利用动态VaR约束控制所面对的风险.运用Bellman动态规划方法和Lagrange乘子法, 得到了该约束问题最优策略的解析式及特殊情形下最优值函数的解析式; 并通过理论分析和数值算例, 阐述了动态VaR约束与随机波动率对最优投资策略的影响.     

全球主要股市波动率的聚类特征分析

本文采用多路归一化割谱聚类方法、单变量GARCH模型和Granger因果检验相结合的模型,分阶段研究了1994-2014年间全球主要股市波动率的聚类特征。首先,利用单变量GARCH模型分别提取全球主要股市的波动率;其次,借助多路归一化割谱聚类方法的特殊性质刻画了全球主要股市波动率的聚类数目、聚类质量以及聚类结果的稳定性等特征;最后,利用Granger因果检验模型分析不同类的代表元股市间的波动溢出效应和同一类内股市间的波动溢出效应。实证结果表明,与非金融危机阶段相比,在金融危机期间全球主要股市波动率的聚类数目较多、聚类质量较高、聚类结果相对稳定、并且全球主要股市间的波动溢出效应增强。     

应用EWMA-GARCH(1,1)-M模型对沪深300股指期货最小VaR套期保值效果研究

VaR是目前国际上应用最广泛的度量金融风险的指标之一,其核心在于波动率,也就是方差的参数估计.采用EWMA模型估计方差,并且结合风险溢价特征的GARCH(1,1)-M模型计算出沪深300股指及其期货的最优衰减因子为0.933 25,摒弃了以往采用0.940 0作为衰减因子的一贯做法,并且运用Cornish-Fisher方程对正态分布的分位数进行了修正,得到修正后的套期保值比率以及资产组合的VaR,与传统的套期保值模型相比,该模型的风险价值VaR降低的程度明显,并且对投资组合未来的VaR具有很好的预测效果,表明EWMA-GARCH(1,1)-M模型对沪深300股指期货的套期保值效果较好.     

Empirical modelling of the DEM/USD and DEM/JPY foreign exchange rate: Structural shifts in GARCH‐models and their implications

We analyse daily changes of two log foreign exchange (FX) rates involving the Deutsche Mark (DEM) for the period 1975–1998, namely FX‐rates measured against the US dollar (USD) and the Japanese yen (JPY). To account for volatility clustering we fit a GARCH(1,1)‐model with leptokurtic innovations. Its parameters are not stable over the sample period and two separate variance regimes are selected for both exchange rate series. The identified points of structural change are close to a change of the monetary policies in the US and Japan, the latter of which is followed by a long period of decreasing asset prices. Having identified subperiods of homogeneous volatility dynamics we concentrate on stylized facts to distinguish these volatility regimes. The bottom level of estimated volatility turns out be considerably higher during the second part of the sample period for both exchange rates. A similar result holds for the average level of volatility and for implied volatility of heavily traded at the money options. Copyright © 2002 John Wiley & Sons, Ltd.