非线性波动模型在上海股票市场中的应用

本文采用非线性GARCH模型研究中国股票市场的波动性。实证结果表明,非线性GARCH模型较传统的线性GARCH模型显著提高了股票市场波动性的描述与预测能力,且非线性GARCH模型的VaR值具有较高的精度,其中以ANSTGARCH模型的效果为最佳。     

台湾股指期货收益波动性与交易量、持仓量考察

采用VAR模型和扩展的GARCH族模型,研究台湾股指期货收益波动性、交易量和持仓量三者之间的动态关系,同时检验交易量和持仓量在GARCH模型中的预测作用。结果表明:台湾股指期货交易量对收益波动性的直接影响存在着滞后效应,波动性间接地依赖于持仓量的变化,交易量和持仓量之间存在明显的双向因果关系。交易量和持仓量的引入能否有助于基础GARCH模型预测收益波动性取决于样本观测期的选择,从均方误差来看三个最好的非样本收益波动性预测模型都是扩展后的GARCH变形模型。     

GARCH模型对沪市行业指数的实证研究

文章中通过基于正态分布和t分布的GARCH模型对沪市行业指数的波动性进行了比较分析,实证结果表明基于t分布的GARCH模型能更精确的描述股市的波动性。此外,文章还用EGARCH模型检验了市场波动的不对称性,实证结果表明沪市行业指数除地产指数外都存在明显的“杠杆效应”,做出市场冲击曲线也能直观说明股票市场的“杠杆效应”。     

基于GARCH类模型对美国股市波动性的对比分析

为研究美国股市股指的波动性特征,本文选取美国股市的Nasdaq指数和Russel2000指数的日收盘价数据,借助统计软件,利用GARCH类模型进行实证分析。实证结果表明：Russel2000指数的风险较Nasdaq指数更稳定,更适合投资,且相较GARCH(1,1)模型,满足学生t分布的APARCH(1,1)模型拟合的条件异方差可以更好地反映种股指日对数收益率的波动率情况,因此可选用此模型对两种指数波动率的未来值进行预测,为投资者提供未来投资参考。     

基于参数与非参数GARCH模型的中国股市波动性预测

本文采用了2003年1月1日——2010年6月30日的上证综合指数和深证成份指数的每日收盘价所得的对数百分收益率为样本,分别运用标准GARCH（1,1）模型和非参数GARCH（1,1）模型[1,3]研究了中国股票市场的波动性,并对这两种模型的估计结果进行了比较,最后利用误差度量指标比较了这两种模型的估计能力,结果发现,非参数GARCH（1,1）模型对股市波动性的预测精度有明显的优势。     

中国开放式基金收益及其波动性的周内效应研究

了解基金收益及其波动性是否存在周内效应对投资者非常重要,投资者可以利用收益及其波动性的变动信息调整投资组合,增加投资收益。运用均值方程含有虚拟变量的GARCH(1,1)模型和条件方差方程含有虚拟变量的修正的GARCH(1,1)模型,我们分别对2003年6月1日至2005年8月18日期间中国开放式基金收益的周内效应和收益波动性的周内效应进行实证研究,结果显示,在研究期间内样本基金收益及收益的波动性在周三这一天显著不同于其他交易日,即存在“周三效应”。     

上证50指数收益率特征及其波动性分析

研究国内非综合指数即成份指数(上证50指数)的收益率特征及其波动性,可以估计得出对指数风险收益具有较好预测作用的自回归———GARCH(1,1)-M模型,并实证分析指数收益的风险特性、稳定性、波动性等特征,这对当前探讨上证50指数相关指数衍生品推出及其投资分析均具有重要意义。     

对韩国股市波动性与宏观经济变量之间关系的实证分析

股市波动性和宏观经济变量之间的关系至今未有定论,本文以GARCH模型和VAR模型来建模,对股市波动性与宏观经济变量变动性之间的关系做出实证分析,结果表明,股市自身历史波动性对于股市当期波动性的解释能力最高,而宏观经济变量的影响很微弱。     

美国道琼斯工业指数的研究和预测——基于时间序列GARCH模型

波动性是诸多经济和金融研究的一个重要方面,GARCH模型适用于具有群集性和方差时变性特点的经济类时间序列数据的回归分析。美国道琼斯工业指数一直是各国参考和衡量股市的重要指标,其波动性的研究结果对投资者选择投资方案时极其重要。文章利用广义自回归模型对美国道琼斯工业指数的波动性进行实证分析。     

股指期货对股票现货市场波动性影响分析

采用事件研究法,构造GARCH(1,1)模型,基于长期数据的基础针对沪深300股指期货的推出对现货市场波动性的影响进行实证研究。经过实证分析得到结论,从长期看来,沪深300股指期货的推出在很小程度上减弱了现货市场股票价格的波动性,但沪深300股指期货的推出却提高了现货市场对于新旧信息的反应效率。     

Forecasting volatility

The forecasting ability of the most popular volatility forecasting models is examined and an alternative model developed. Existing models are compared in terms of four attributes: (1) the relative weighting of recent versus older observations, (2) the estimation criterion, (3) the trade‐off in terms of out‐of‐sample forecasting error between simple and complex models, and (4) the emphasis placed on large shocks. As in previous studies, we find that financial markets have longer memories than reflected in GARCH(1,1) model estimates, but find this has little impact on outofsample forecasting ability. While more complex models which allow a more flexible weighting pattern than the exponential model forecast better on an in‐sample basis, due to the additional estimation error introduced by additional parameters, they forecast poorly out‐of‐sample. With the exception of GARCH models, we find that models based on absolute return deviations generally forecast volatility better than otherwise equivalent models based on squared return deviations. Among the most popular time series models, we find that GARCH(1,1) generally yields better forecasts than the historical standard deviation and exponentially weighted moving average models, though between GARCH and EGARCH there is no clear favorite. However, in terms of forecast accuracy, all are dominated by a new, simple, nonlinear least squares model, based on historical absolute return deviations, that we develop and test here. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:465–490, 2005     

Information content of volatility spreads

This study reexamines the determinants of volatility spreads and suggests a new forecast of future volatilities. Contrary to earlier volatility forecasts, the newly introduced forecast is applicable when investors are not risk‐neutral or when underlying returns do not follow a Gaussian probability distribution. This implies that the method is consistent with the presence of risk premia for other risks such as volatility risk. Using S&P 500 index options, we show that the new volatility forecast outperforms other volatility forecasts including risk‐neutral implied volatility and historical volatility in two aspects. First, the new forecast is superior to other estimates in terms of forecasting errors for future realized volatilities. Second, it is an unbiased estimator of future realized volatilities. This is shown using an encompassing regression analysis. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:533–558, 2010     

Conditional Volatility and the GARCH Option Pricing Model with Non‐Normal Innovations

On the basis of the theory of a wedge between the physical and risk‐neutral conditional volatilities in Christoffersen, P., Elkamhi, R., Feunou, B., & Jacobs, K. (2010), we develop a modification of the GARCH option pricing model with the filtered historical simulation proposed in Barone‐Adesi, G., Engle, R. F., & Mancini, L. (2008). The one‐day‐ahead conditional volatilities under physical and risk‐neutral measures are the same in the previous model, but should have been allowed to be different. Using extensive data on S&P 500 index options, our approach, which employs one‐day‐ahead risk‐neutral conditional volatility estimated from the cross‐section of the option prices (in contrast to the existing GARCH option pricing models), maintains theoretical consistency under conditional non‐normality, and improves the empirical performances. Remarkably, the risk‐neutral volatility dynamics are stable over time in this model. In addition, the comparison between the VIX index and the risk‐neutral integrated volatility economically validates our approach. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 33:1–28, 2013     

APPROXIMATING GARCH-JUMP MODELS, JUMP-DIFFUSION PROCESSES, AND OPTION PRICING

This paper considers the pricing of options when there are jumps in the pricing kernel and correlated jumps in asset prices and volatilities. We extend theory developed by Nelson (1990) and Duan (1997) by considering the limiting models for our approximating GARCH Jump process. Limiting cases of our processes consist of models where both asset price and local volatility follow jump diffusion processes with correlated jump sizes. Convergence of a few GARCH models to their continuous time limits is evaluated and the benefits of the models explored.     

VIX futures and its closed‐form pricing through an affine GARCH model with realized variance

This paper studies the forecasting of volatility index (VIX) and the pricing of its futures by a generalized affine realized volatility model proposed by Christoffersen et al. This model is a weighted average of a GARCH and a pure realized variance (RV) model that incorporates each volatility component into the new dynamics. We rewrite the VIX in terms of both volatility components and then derive closed‐form formulas for the VIX forecasting and its futures pricing. Our empirical studies find that a unification of the GARCH and the RV in the modeling substantially improves the forecasting of this index and the pricing of its futures.     

Return distributions and volatility forecasting in metal futures markets: Evidence from gold,silver, and copper

The characterization of return distributions and forecast of asset‐price variability play a critical role in the study of financial markets. This study estimates four measures of integrated volatility—daily absolute returns, realized volatility, realized bipower volatility, and integrated volatility via Fourier transformation (IVFT)—for gold, silver, and copper by using high‐frequency data for the period 1999 through 2008. The distributional properties are investigated by applying recently developed jump detection procedures and by constructing financial‐time return series. The predictive ability of a GARCH (1,1) forecasting model that uses various volatility measures is also examined. Three important findings are reported. First, the magnitude of the IVFT volatility estimate is the greatest among the four volatility measures. Second, the return distributions of the three markets are not normal. However, when returns are standardized by IVFT and realized volatility, the corresponding return distributions bear closer resemblance to a normal distribution. Notably, the application of financial‐time sampling technique is helpful in obtaining a normal distribution. Finally, the IVFT and realized volatility proxies produce the smallest forecasting errors, and increasing the time frequency of estimating integrated volatility does not necessarily improve forecast accuracy. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:55–80, 2011     

汇改对我国中小企业出口的影响测度与预测——基于汇改后月度数据的实证分析

当前我国中小企业出口经营困境凸显,进一步汇改是否会加剧其困境成为关注的焦点。本文基于汇改后的月度数据,采用GARCH模型分析各次汇改对汇率弹性的影响特征,构建向量误差修正模型测度和预测汇改对中小企业出口的影响。结果表明:汇改促使人民币每升值1%,其出口减少3.874%;汇率弹性增强1%,其出口减少0.034%。预测的中小企业出口总额较为平稳。进一步汇改以增强汇率弹性为核心不会对中小企业出口总量造成大的冲击。     

The bias in time series volatility forecasts

By Jensen's inequality, a model's forecasts of the variance and standard deviation of returns cannot both be unbiased. This study explores the bias in GARCH type model forecasts of the standard deviation of returns, which we argue is the more appropriate volatility measure for most financial applications. For a wide variety of markets, the GARCH, EGARCH, and GJR (or TGARCH) models tend to persistently over‐estimate the standard deviation of returns, whereas the ARLS model of L. Ederington and W. Guan (2005a) does not. Furthermore, the GARCH and GJR forecasts are especially biased following high volatility days, which cause a large jump in forecast volatility, which is rarely fully realized. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:305–323, 2010     

A No‐Arbitrage Fractional Cointegration Model for Futures and Spot Daily Ranges

The no‐arbitrage relation between futures and spot prices implies an analogous relation between futures and spot daily ranges. The long‐memory features of the range‐based volatility estimators are analyzed, and fractional cointegration is tested in a semi‐parametric framework. In particular, the no‐arbitrage condition is used to derive a long‐run relationship between volatility measures and to justify the use of a fractional vector error correction model (FVECM) to study their dynamic relationship. The out‐of‐sample forecasting superiority of FVECM, with respect to alternative models, is documented. The results highlight the importance of incorporating the long‐run equilibrium in volatilities to obtain better forecasts, given the information content in the volatility of futures prices. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 33:77–102, 2013     

The forecast quality of CBOE implied volatility indexes

We examine the forecast quality of Chicago Board Options Exchange (CBOE) implied volatility indexes based on the Nasdaq 100 and Standard and Poor's 100 and 500 stock indexes. We find that the forecast quality of CBOE implied volatilities for the S&P 100 (VXO) and S&P 500 (VIX) has improved since 1995. Implied volatilities for the Nasdaq 100 (VXN) appear to provide even higher quality forecasts of future volatility. We further find that attenuation biases induced by the econometric problem of errors in variables appear to have largely disappeared from CBOE volatility index data since 1995. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:339–373, 2005