PARAMETER ESTIMATION FOR A DISCRETELY OBSERVED STOCHASTIC VOLATILITY MODEL WITH JUMPS IN THE VOLATILITY

In this paper a stochastic volatility model is considered. That is, a log price process Y which is given in terms of a volatility process V is studied. The latter is defined such that the log price possesses some of the properties empirically observed by Barndorff-Nielsen & Jiang[6]. In the model there are two sets of unknown parameters, one set corresponding to the marginal distribution of V and one to autocorrelation of V. Based on discrete time observations of the log price the authors discuss how to estimate the parameters appearing in the marginal distribution and find the asymptotic properties.     

TESTING FOR VARYING DISPERSION OF LONGITUDINAL BINOMIAL DATA IN NONLINEAR LOGISTIC MODELS WITH RANDOM EFFECTS

In this paper, it is discussed that two tests for varying dispersion of binomial data in the framework of nonlinear logistic models with random effects, which are widely used in analyzing longitudinal binomial data. One is the individual test and power calculation for varying dispersion through testing the randomness of cluster effects, which is extensions of Dean(1992) and Commenges et al (1994). The second test is the composite test for varying dispersion through simultaneously testing the randomness of cluster effects and the equality of random-effect means. The score test statistics are constructed and expressed in simple, easy to use, matrix formulas. The authors illustrate their test methods using the insecticide data (Giltinan, Capizzi & Malani (1988)).     

A NOTE ON THE STRONG CONSISTENCY OF ESTEMATES IN PARTIALLY LINEAR MODELS

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THE AVALANCHE DYNAMICS IN RANDOM NEAREST NEIGHBOR MODELS OF EVOLUTION WITH INTERACTION STRENGTH

A generalized Bak-Sneppen model (BS model) of biological evolution with interaction strength θ is introduced in d-dimensional space, where the "nearest neighbors" are chosen among the 2d neighbors of the extremal site, with the probabilities related to the sizes of the fitnesses. Simulations of one- and two-dimensional models are given. For given θ > 0, the model can self-organize to a critical state, and the critical threshold fc(θ) decreases as θ increases. The exact gap equation depending on θ is presented, which reduces to the gap equation of BS model as θ tends to infinity. An exact equation for the critical exponent γ(θ) is also obtained. Scaling relations are established among the six critical exponents of the avalanches of the model.     

RATES OF A.S.CONVERGENCE OF THE ESTIMATION OF ERROR VARIANCE IN LINEAR MODELS

Under appropriate conditions we obtain the best rates of a.s.convergence of estimates5_n~2 of error variance σ~2 and establish the law of iterated logarithm     

A COMPARISON BETWEEN TWO ROBUST REGRESSION ESTIMATORS BY MEANS OF ROBUST COVARIANCES

Two classes of Mallows GM-estimators with invariance are considered in the stochastic linear regression model. Some of their asymptotic properties are described, and the fittedvalue influence and variance components are compared by means of robust covariances,     

THE EXISTENCE OF POSITIVE PERIODIC SOLUTIONS IN A LOGISTIC DIFFERENCE MODEL WITH A FEEDBACK CONTROL

Consider the following nonautonomous delayed periodic logistic difference model with feedback control termwhich describes the evolution of a single species. The existence of a positive periodic solution is established by using the method of Mawhin's coincidence degree. This work has important significance in both theory and applications.     

A CASE STUDY IN THE APPLICATION OF SUPERSATURATED DESIGNS TO COMPUTER EXPERIMENTS

Supersaturated design is essentially a fractional factorial design in which the number of potential effects is greater than the number of runs. In this article, the supersaturated design is applied to a computer experiment through an example of steady current circuit model problem. A uniform mixed-level supersaturated design and the centered quadratic regression model are used. This example shows that supersaturated design and quadratic regression modeling method are very effective for screening effects and building the predictor. They are not only useful in computer experiments but also in industrial and other scientific experiments.     

TESTING OF CORRELATION AND HETEROSCEDASTICITY IN NONLINEAR REGRESSION MODELS WITH DBL（p,q, 1） RANDOM ERRORS

Chaos theory has taught us that a system which has both nonlinearity and random input will most likely produce irregular data. If random errors are irregular data, then random error process will raise nonlinearity （Kantz and Schreiber （1997））. Tsai （1986） introduced a composite test for autocorrelation and heteroscedasticity in linear models with AR（1） errors. Liu （2003） introduced a composite test for correlation and heteroscedasticity in nonlinear models with DBL（p, 0, 1） errors. Therefore, the important problems in regression model axe detections of bilinearity, correlation and heteroscedasticity. In this article, the authors discuss more general case of nonlinear models with DBL（p, q, 1） random errors by score test. Several statistics for the test of bilinearity, correlation, and heteroscedasticity are obtained, and expressed in simple matrix formulas. The results of regression models with linear errors are extended to those with bilinear errors. The simulation study is carried out to investigate the powers of the test statistics. All results of this article extend and develop results of Tsai （1986）, Wei, et al （1995）, and Liu, et al （2003）.     

PRICING EUROPEAN OPTION IN A DOUBLE EXPONENTIAL JUMP-DIFFUSION MODEL WITH TWO MARKET STRUCTURE RISKS AND ITS COMPARISONS

Using Fourier inversion transform, P.D.E. and Feynman-Kac formula, the closedform solution for price on European call option is given in a double exponential jump-diffusion model with two different market structure risks that there exist CIR stochastic volatility of stock return and Vasicek or CIR stochastic interest rate in the market. In the end, the result of the model in the paper is compared with those in other models, including BS model with numerical experiment. These results show that the double exponential jump-diffusion model with CIR-market structure risks is suitable for modelling the real-market changes and very useful.     

宏观经济信息宣告的股市收益及波动性效应——基于改进的AR(1)-EGARCH(1,1)-M模型的实证检验

基于改进的AR(1)-EGARCH(1,1)-M模型,从收益率和波动性两个方面考察各类宏观信息宣告对股票市场价格行为的影响.结果表明,居民消费价格指数和商品零售价格指数对股票市场的收益有负向影响;国内生产总值、社会消费品零售总额、公开市场操作利率变动率和企业景气指数对股票市场的收益有正向影响;公开市场操作公告会导致股票市场条件收益率显著增加;其余各类宏观信息因素对股票市场收益的波动性并不存在显著影响.     

中国股票市场风险的实证分析研究

本文从实证角度说明了上证指数和深证成份指数存在着GARCH现象 ,并建立了沪、深两市股指波动率的IGARCH(1,1) M模型与EGARCH(1,1) M模型。将估计的IGARCH(1,1) M模型与EGARCH(1,1) M模型比较得出 ,对上证指数的波动率 ,IGARCH(1,1) M模型与EGARCH(1,1) M模型的模拟效果基本相同 ,而对深证成份指数的波动率 ,IGARCH M模型要略优于EGARCH M模型。同时还对两市的股指收益的波动率进行了预测分析     

A mathematical analysis of the Gumbel test for jumps in stochastic volatility models

This article gives an exhaustive mathematical analysis of the Gumbel test for additive jump components based on extreme value theory. The Gumbel test was first introduced by Lee and Mykland in 2008 from an economical point of view. They consider a continuous-time stochastic volatility model with a general continuous volatility process and observe it under a high-frequency sampling scheme. The test statistics based on the maximum of increments converges to the Gumbel distribution under the null hypothesis of no additive jump component and to infinity otherwise. Our article presents a moment method based technique that provides some deeper mathematical insights into the convergence and divergence case of the test statistics. In the non-jump case we are able to prove the convergence to the Gumbel distribution under greatly weak assumptions: The volatility process has to be merely pathwise Hölder continuous with an arbitrary random Hölder exponent and we have no restrictions concerning an additional drift term. Therefore, for example, we are allowing for long and short-range dependence. In the case of existing additive jumps, we give divergence results in a general semimartingale setting and investigate the speed of divergence depending on the jump activity. As a by-product of our analysis we also deduce an optimal pathwise estimator for the spot volatility process. Moreover, we provide a detailed simulation study that compares the power of the Gumbel test with the power of the jump test proposed by Barndorff–Nielsen and Shephard in 2006 for Hölder exponents close to zero. Finally, both tests are applied to a real dataset.     

沪、深股市波动不对称性的实证分析

本支应用系数多变量EGARCH模型来研究我国沪深股市的波动不对性,结果发现:在全样本时期,收益率呈现深市向沪市的单向溢出,而沪深两市则都呈现显著的波动不对称性特征。分时段来考察,B股对境内投资者开放前后呈现收益率由深市向沪市的单向溢出到双向溢出现象;而波动性的实证结果则显示,以B股对境内投资者开放为间断点,沪市波动不对称性有明显加强的趋势,而深市波动不对称性则呈现由不显著到显著的特征。     

有效矩估计在中国股票市场的应用研究

对期权定价模型的一类拓展模型-随机波动率(SV)模型,由于模型中存在不可观测的随机波动因素,并且其精确似然函数很难得到,于是提出了一种基于标的资产价格历史数据的有效矩估计(EMM)方法,此方法是把观测数据映射到简化的辅助模型GARCH(1,1)上,并计算辅助模型得分用以建立矩条件,实现SV模型参数的有效估计.利用这一方法对中国股市进行了波动分析,得出了较好的结果.     

沪深股市杠杆效应的实证分析

运用 E-GARCH模型对沪深股市的杠杆效应进行了实证分析 ,结果表明 ,日收益存在着明显的杠杆效应 ,收益对波动强度的影响具有非对称性 .     

中国股市期权波动率微笑特征的实证分析

波动率微笑现象显示了期权隐含波动率和执行价格之间的关系.在理想的完全符合Black-Scholes期权定价模型假设的情况下,期权隐含波动率关于执行价格应该是一条水平线.然而,在实证分析中,对隐含波动率和执行价格进行拟合并绘制曲线,会产生一个倾斜或微笑形状的曲线,证明Black-Scholes期权定价模型存在一定的缺陷....     

固定设计下非参数回归模型估计的渐近性质

考虑固定设计下具有非参数AR(1)的非参数回归模型,综合最小二乘和非参数核估计法,定义了非参数函数的估计量,在适当的条件下,研究了它们的渐近性质.     

一种广义的二元混合分布模型在中国股票市场的应用研究

首次引入一种广义的二元混合分布模型,从信息经济学的视角揭示中国股票市场价格波动与交易量的动态特征及联合分布.结论显示,Tauchen and Pitts的标准二元混合模型在捕捉价格波动的持续性上还存在一定的缺陷,而Liesenfeld提出的广义二元混合模型(GBMM)明显优于标准二元混合模型,我们还对GBMM模型进行了再扩展.