上海股票市场收益的随机波浪模型

对金融资产收益分布状况的主要研究方法是先提出分布模型,然后进行实验验证;因缺乏必要的机理分析和研究手段单一,使其理论研究和应用研究都受到一定的制约.为克服这些不足,将金融资产收益联系起来看,根据其涨跌周期性构建出随机波浪模型,并利用模型导出随机波浪波高和周期的分布公式.通过实证分析,证明随机波浪模型具有一定的适用性;所用的时频分析方法以及所得结论有益于对金融资产收益分布状况进行更深入的理论和应用研究,也有益于指导市场参与者进行短期和长期交易.     

沪深股市相关结构分析研究

在金融市场风险分析中,对金融资产相关结构的讨论有着重要意义,从而引出对如何选取好的相关结构模型来捕捉金融资产间的相关变化规律的讨论。针对这一问题,我们用混合相关结构函数Copula对上海、深圳股票市场进行了相关分析研究,用极值分布刻画了每支股票的边缘分布,用两步估计法对Copula中的参数进行了估计。分析结果表明:混合Copula相关结构能够捕捉金融市场间相关性变化规律,比单个Copula相关结构更灵活,更能全面地反映市场间非对称变化的相关程度和模式,此方法还可以推广到对多种金融资产收益率进行相关性分析。     

基于改进ICA模型的高维波动率估计

本文对IC-GARCH模型进行改进,放宽了ICA关于独立成分是IID的假设,考虑独立成分为ARMA模型的平稳过程,提出了基于自相关结构的IC-GARCH估计方法,并给出了估计量的理论性质和计算效率较高的迭代估计算法。最后,对改进方法进行了模拟和实证分析,结果表明本文提出的模型能够使多元GARCH模型应用于高维金融数据,并大大提高了金融资产收益波动率的估计精度。     

半参数门限广义非对称随机波动模型研究

为了能够同时刻画和描述金融资产收益序列的偏态、厚尾以及序列的门限效应、非对称杠杆效应等特性,提出把门限广义非对称随机波动模型与非参数Dirichlet过程混合模型有机结合,构建了半参数门限广义非对称随机波动模型,并对模型进行了贝叶斯分析.实证研究中,利用上海黄金价格收益率序列数据进行建模分析,结果表明:半参数门限广义非对称随机波动模型能够有效地刻画上海黄金价格收益率序列波动率的动态特征.     

基于MCMC抽样的金融贝叶斯半参数GARCH模型研究

GARCH模型是研究金融资产收益的重要模型,然而现有参数GARCH模型依然不能有效刻画金融资产收益偏态厚尾特性且存在模型设定风险。本文在非参数分布和GARCH模型基础上,建立半参数GARCH模型以提高模型的有效性;同时在贝叶斯框架内发展有效MCMC抽样解决模型的参数估计难问题,并利用DIC4研究模型比较问题;最后通过模拟研究和实证研究考察MCMC抽样的有效性,检验半参数GARCH模型在刻画金融资产收益特性和风险价值预测方面的实际效果。     

基于混合Copula的CDO定价模型

将广受欢迎的,用于CDO定价的大样本同质投资组合近似方法做了推广,其中涉及到的分布是高斯分布和Variance Gamma分布的混合,即G-VG混合分布.提出了厚尾的G-VG混合Copula模型和带有随机相关性的混合模型.这些模型可以有效的模拟CDO定价中的"相关性微笑"问题.在这些G-VG混合Copula模型中,得到了损失分布函数和期望分券层损失的解析表达式.并且用实际数据做了实证分析,把新模型和高斯模型的结果做了比较.实证表明,新模型的结果不仅与市场报价更贴近,而且为相关性结构带来了更多的灵活性.     

金融资产多分辨风险识别及投资组合策略

为有效地揭示金融市场微观结构、反映和分散金融风险,基于最大重复离散小波变换对高频数据进行了多分辨分析,利用小波方差和小波协方差给出多分辨Beta系数的计算方法,讨论了高频金融资产不同时间尺度下的风险组成。针对收益与风险的多分辨特征,提出多分辨投资组合策略,改进了Markowitz的静态投资组合方法。实证研究表明,同一金融资产在不同时间尺度下的收益与风险存在多分辨特征;CAPM的表现也具有多分辨特征;而多分辨的投资组合策略则将不同时间尺度下的投资风险降到了最低。     

状态转移框架下跨地区、跨行业资产配置模型及实证

利用Markov状态转移模型捕捉金融资产收益率序列的非线性、动态的结构性变化,考虑不同市场状态下资金在地区板块、行业板块间流动导致的板块轮动效应,构建基于状态转移的跨地区、跨行业资产配置模型。在此基础上,对市场状态和地区、行业板块轮动效应对资产配置的影响进行细致分析。研究发现:中国股票市场存在明显的动态结构性变化,可以分为熊市状态和牛市状态,两种市场状态下最优资产配置结构不同。结果表明,状态转移框架下的跨地区和跨行业资产配置能够刻画非对称市场状态下资产的收益和风险特征,分散非系统性风险的同时降低市场风险,提高投资者的收益,可以为投资者决策提供有价值的参考。     

ρ*-混合序列加权和的完全收敛性

讨论了ρ*-混合序列加权和的完全收敛性,将文[8]中的定理3推广至ρ*-混合序列的情形且加强了文[8]中的定理3的结论.将文[9]中的定理推广至ρ*-混合序列的情形.     

基于帕累托分布的聚合收益率的VaR计算方法

极值理论在金融资产收益分析中有着重要应用,金融资产收益率的厚尾分布可以用帕累托分布来描述,但是在计算投资组合的VaR时,需要知道的是组合的分布,但是其具体的分布形式却是不可知的.所以本文就在先前研究的基础之上通过对帕累托总和进行分解得到2个分解总和,通过对这2个总和的分析求得其各自的分布,再由此计算出总和的近似分布,从而求得投资组合的VaR.这种方法不仅考虑了每个个体对总和的影响力度,还弥补了极端事件对结果的影响,使得计算出来的VaR值对市场风险的衡量更为的准确.     

Correcting statistical models via empirical distribution functions

We consider the two-sample homogeneity problem where the information contained in two samples is used to test the equality of the underlying distributions. In cases where one sample is simulated by a procedure modelling the data generating process of another observed sample, a mere rejection of the null hypothesis is unsatisfactory. Instead, the data analyst would like to know how the simulation can be improved. Based on the popular Kolmogorov–Smirnov test and a general mixture model, we propose an algorithm that determines an appropriate correction distribution function. Complementing the simulation sample by a given proportion of observations sampled from this distribution reduces the Kolmogorov–Smirnov distance between the modified and the observed sample. Therefore, the correction distribution indicates possible improvements to the current simulation process. We prove our algorithm to run in linear time when applied to sorted samples. We further illustrate its intuitive results on simulated as well as on real data sets from astrophysics and bioinformatics.     

Hodges-Lehmann asymptotic efficiency of the Kolmogorov and Smirnov goodness-of-fit tests

One considers the Hodges-Lehmann asymptotic efficiency of the Kolmogorov and Smirnov goodness-of-fit tests, which measures the rate of the exponential decrease of the errors of the second kind, under a fixed significance level. It is shown that the Kolmogorov test is always asymptotically optimal in this sense, while the one-sided Smirnov test is asymptotically optimal under additional conditions imposed on the parametric family of distributions.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 142, pp. 119–123, 1985.     

A constructive hypothesis test for the single-index models with two groups

Comparison of two-sample heteroscedastic single-index models, where both the scale and location functions are modeled as single-index models, is studied in this paper. We propose a test for checking the equality of single-index parameters when dimensions of covariates of the two samples are equal. Further, we propose two test statistics based on Kolmogorov–Smirnov and Cramér–von Mises type functionals. These statistics evaluate the difference of the empirical residual processes to test the equality of mean functions of two single-index models. Asymptotic distributions of estimators and test statistics are derived. The Kolmogorov–Smirnov and Cramér–von Mises test statistics can detect local alternatives that converge to the null hypothesis at a parametric convergence rate. To calculate the critical values of Kolmogorov–Smirnov and Cramér–von Mises test statistics, a bootstrap procedure is proposed. Simulation studies and an empirical study demonstrate the performance of the proposed procedures.     

Limit distributions and comparative asymptotic efficiency of the Smirnov — Kolmogorov statistics with a random index

Limit distributions for certain statistics of Smirnov — Kolmogorov type are obtained which consider the weak convergence of the corresponding empirical process. Approximate and precise asymptotic efficiencies of these statistics are computed. It is shown that they are worse in a certain sense than the classical Kolmogorov — Smirnov statistics.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 55, pp. 185–194, 1976.     

Numerical comparison of classical and permutation statistical hypothesis testing methods

The article is devoted to the classical problem of statistical hypothesis testing for the equality of two distributions. For normal distributions, Student’s test is optimal in many senses. However, in practice, distributions to be compared are often not normal and, generally speaking, unknown. When nothing is known about the distributions to be compared, one usually applies the nonparametric Kolmogorov–Smirnov test to solve this problem. In the present paper, methods are considered that are based on permutations and, in recent years, have attracted interest for their simplicity, universality, and relatively high efficiency. Methods of stochastic simulation are applied to the comparative analysis of the power of a few permutation tests and classical methods (such as the Kolmogorov–Smirnov test, Student’s test, and the Mann–Whitney test) for a wide class of distribution functions. Normal distributions, Cauchy distributions, and their mixtures, as well as exponential, Weibull, Fisher’s, and Student’s distributions are considered. It is established that, for many typical distributions, the permutation method based on the sum of the absolute values of differences is the most powerful one. The advantage of this method over other ones is especially large when one compares symmetric distributions with the same centers. Thus, this permutation method can be recommended for application in cases when the distributions to be compared are different from normal ones.     

GH分布族下资产收益率分布拟合优度比较——基于中国证券指数高频数据的实证研究

资产收益率分布假设对期权定价、对冲,风险度量和组合资产优化的结果有着重要影响.但由于资产收益率的"程式化性质",经典正态分布假设不能很好拟合实际收益率分布.广义双曲线分布,作为子分布及极限分布非常丰富的分布族,在资产收益率分布拟合中已取得良好效果.在讨论第三类修正贝塞尔函数和广义逆高斯分布性质基础上,借助于正态均值-方差混合理论,得到广义双曲线分布及其极限分布.在McNeil,Frey和Embrechts(2005)算法框架内,以及WenBo Hu(2005)算法改进基础上,对参数估计的算法做了实质性改进:用两个重要参数χ和ψ的线性关系,代替了一个包含第三类修正贝塞尔函数的方程,避免了对该方程数值求解.在实证部分,选择了3个主要指数,利用GH分布的两个子分布和两个极限分布对过滤后的指数收益率进行拟合,并对它们的拟合优度和收敛速度做了比较.     

Two New Mixture Models Related to the Inverse Gaussian Distribution

This article presents a new family of logarithmic distributions to be called the sinh mixture inverse Gaussian model and its associated life distribution referred as the extended mixture inverse Gaussian model. Specifically, the density, distribution function, and moments are developed for the sinh mixture inverse Gaussian distribution. Next, the extended mixture inverse Gaussian distribution is characterized. A graphical analysis of the densities of the new models is also provided. In addition, a lifetime analysis is presented for the extended mixture inverse Gaussian distribution. Finally, an example with a real data set is given to illustrate the methodology, which indicates that the new models result in a better fit to the data than some other well-known distributions.     

Jump diffusion processes and their applications in insurance and finance

For insurance risks, jump processes such as homogeneous/non-homogeneous compound Poisson processes and compound Cox processes have been used to model aggregate losses. If we consider the economic assumption of a positive interest to aggregate losses, Lévy processes have proven to be useful. Also in financial modelling, it has been observed that diffusion models are not robust enough to capture the appearance of jumps in underlying asset prices and interest rates. As a result, jump diffusion processes, which are, simply speaking, combinations of compound Poisson processes with Brownian motion, have gained popularity for modelling in insurance and finance. In this paper, considering a jump diffusion process, we obtain the explicit expression of the joint Laplace transform of the distribution of a jump diffusion process and its integrated process, assuming that jump size follows the mixture of two exponential distributions, which is a special case of phase-type distributions. Based on this Laplace transform, we derive the moments of the aggregate accumulated claim amounts of insurance risk. For a financial application, we concern non-defaultable zero-coupon bond pricing. We also provide several numerical examples for the moments of aggregate accumulated claims and default-free zero-coupon bond prices.     

Nonparametric evaluation of the first passage time of degradation processes

This paper discusses a nonparametric method to approximate the first passage time (FPT) distribution of the degradation processes incorporating random effects if the process type is unknown. The FPT of a degradation process is unnecessarily observed since its density function can be approximated by inverting the empirical Laplace transform using the empirical saddlepoint method. The empirical Laplace transform is composed of the measured increments of the degradation processes. To evaluate the performance of the proposed method, the approximated FPT is compared with the theoretical FPT assuming a true underlying process. The nonparametric method discussed in this paper is shown to possess the comparatively small relative errors in the simulation study and performs well to capture the heterogeneity in the practical data analysis. To justify the fitting results, the goodness‐of‐fit tests including Kolmogorov‐Smirnov test and Cramér‐von Mises test are conducted, and subsequently, a bootstrap confidence interval is constructed in terms of the 90th percentile of the FPT distribution.     

随机利率下基于Tsallis熵分布的幂式期权定价

考虑到无风险利率的随机性以及股票收益率分布的尖峰厚尾和长期相依性,利用具有长程记忆及统计反馈性质的Tsallis熵分布建立股票价格的运动模型,在无风险利率服从Vasicek模型下,运用保险精算定价法得到了幂式期权的定价公式,推广了经典的Black-Scholes定价公式,扩展了已有文献的结论.