协方差矩阵最佳仿射同变估计的改进

§1.引言 Stein(1964)证明了正态分布的方差的最佳仿射同变估计的不容许性.Shorrock和Zidek(1976)给出了正态分布的广义方差的最佳仿射同变估计的一个改进估计.本文推广了他们的结果,对正态分布的协方差矩阵的最佳仿射同变估计进行了改进.     

基于结构突变的波动率分解模型

在Heston-Nandi模型的基础上提出了一种波动率分解模型,分解模型同时考虑了金融波动的长记忆性和杠杆效应.从资产收益率的无条件方差发生结构突变出发,认为收益率的无条件方差随时间变化,将波动率分解为长期影响和短期冲击两部分,其中长期影响用来刻画波动率的持续性,短期冲击刻画金融波动的短期扰动.上证综指数据实证表明上海证券综合指数收益率序列的波动性同时具有长记忆性和杠杆效应,利用模型能很好的刻画这两种性质.     

ARCH族模型对沪市行业指数收益率的实证研究

本文利用ARCH族模型研究沪市行业指数收益率的波动性.通过对各行业指数收益率的分析发现,行业指数收益率是平稳的,但其条件方差是尖峰厚尾的非正态分布且具有明显的ARCH效应.行业指数收益率均具有不同程度"杠杆"效应.外部信息对公用指数和综合指数收益率影响最大.融入相同的风险,它们收益最高.地产指数对外部信息反应迟钝,收益率也不显著.     

深证成指周收益率波动性的实证研究

利用GARCH模型,对深圳成分指数的周收益率波动性进行了实证研究。以深证成指周收盘数据建立了GARCH模型,利用估计出的GARCH模型得到深证成指周收益率序列的条件方差的估计值,预测出深证成指周收益率序列未来若干期的条件方差。结果表明,深证成指周收益率序列的波动性可以用GARCH模型进行很好的拟合。     

沪深股市大盘指数收益率分布尾部的实证研究

通过H ill估计的改进方法对上证综合指数和深圳成分指数的收益率分布的尾部指数进行了参数估计,用χ2检验验证了指数的稳定性及其置信区间.在此基础上提出用尾部指数估计尾概率,达到风险控制的目的.实证研究表明,沪深大盘指数收益率分布具有肥尾的特征,但并不服从无限方差分布.     

教育收益率估计方法的比较

本文对教育经济学中个人教育投资明瑟收益率的估计方法进行了比较研究,特别是引入了部分线性回归模型对明瑟收益率进行估计的方法,并且通过广义似然比检验对常规明瑟模型中的参数形式进行了检验。     

随机权函数半参数回归模型的导方差统计分析

在回归分析中,观测值的方差齐性只是一个基本的假定,在参数、半参数和非参数回归模型中关于异方差检验和估计问题已有很多研究.本文在冉昊和朱忠义(2004)讨论的半参数回归模型的基础上,用随机参数方法,讨论随机权函数半参数回归模型中的异方差检验问题,得到了方差齐性检验Score统计量,同时,当半参数模型存在异方差时,本文还给出了估计方差的方法.     

线性混合模型中固定效应和方差分量同时最优估计

对于具有广泛应用的含有两个方差分量的线性混合模型, 找到了一组简单条件. 在这些条件下, 证明了固定效应的最小二乘估计和方差分量的方差分析估计同时是最小方差无偏估计; 获得了固定效应的精确置信区间和随机效应的方差分量的一致最优无偏检验; 得到了随机效应方差的方差分析估计取负值的概率精确表达式.     

基于M估计的指数相关非线性混合效应模型的齐性检验(英文)

方差和相关系数的齐性是纵向数据分析中常用假设之一,然而,这些假设未必合适.本文主要研究的是具有指数相关结构的纵向数据非线性混合效应模型,首先将Huber函数引入模型的对数似然函数中,利用Fisher得分迭代法得到模型参数的稳健估计(M估计),然后基于M估计对模型的方差和相关系数的齐性进行了Score检验,并给出了检验统计量的Monte-Carlo模拟结果.最后用一个实例说明了本文的方法.     

比例优势模型在多结局区间截断数据上的应用

探索比例优势模型在临床医学中常见的多结局区间截断数据中的应用.用条件的逻辑回归方法避免讨厌参数的估计,用牛顿-拉普森算法估计回归系数,用＂夹心方差＂估计量作为参数方差的估计.通过随机模型检验模型应用的有效性.     

Stochastic volatility Gaussian Heath-Jarrow-Morton models

This paper extends the class of deterministic volatility Heath-Jarrow-Morton models to a Markov chain stochastic volatility framework allowing for jump discontinuities and a variety of deformations of the term structure of forward rate volatilities. Analytical solutions for the dynamics of the volatility term structure are obtained. Semimartingale decompositions of the interest rates under a spot and forward martingale measures are identified. Stochastic volatility versions of the continuous time Ho-Lee and Hull-White extended Vasicek models are obtained. Introducing a regime shift in volatility that is an exponential function of time to maturity leads to a Vasicek dynamics with regime switching coefficients of the short rate.     

Long-term and blow-up behaviors of exponential moments in multi-dimensional affine diffusions

This paper considers multi-dimensional affine processes with continuous sample paths. By analyzing the Riccati system, which is associated with affine processes via the transform formula, we fully characterize the regions of exponents in which exponential moments of a given process do not explode at any time or explode at a given time. In these two cases, we also compute the long-term growth rate and the explosion rate for exponential moments. These results provide a handle to study implied volatility asymptotics in models where log-returns of stock prices are described by affine processes whose exponential moments do not have an explicit formula.     

Medium‐term horizon volatility forecasting: A comparative study

In this paper, volatility is estimated and then forecast using unobserved components‐realized volatility (UC‐RV) models as well as constant volatility and GARCH models. With the objective of forecasting medium‐term horizon volatility, various prediction methods are employed: multi‐period prediction, variable sampling intervals and scaling. The optimality of these methods is compared in terms of their forecasting performance. To this end, several UC‐RV models are presented and then calibrated using the Kalman filter. Validation is based on the standard errors on the parameter estimates and a comparison with other models employed in the literature such as constant volatility and GARCH models. Although we have volatility forecasting for the computation of Value‐at‐Risk in mind the methodology presented has wider applications. This investigation into practical volatility forecasting complements the substantial body of work on realized volatility‐based modelling in business. Copyright © 2007 John Wiley & Sons, Ltd.     

不同矩属性波动模型对中国股市波动率的预测精度分析

金融时间序列的波动性建模经历了从一阶矩到二阶矩直到高阶矩(包含三阶矩和四阶矩)的过程,而对于高阶矩波动模型是否有助于对未来市场的波动率预测这一问题,国内外学术界尚无文献讨论。以上证综指长达7年的每5分钟高频数据样本为例,通过构建具有不同矩属性的波动模型,计算了中国股票市场波动率的预测值,并利用具有bootstrap特性的SPA检验法,实证检验了不同矩属性波动模型的波动率预测精度差异。实证结果显示:就中国股市而言,四阶矩波动模型能够取得比二阶矩波动模型更优的波动率预测精度,而三阶矩波动模型并未表现出比二阶矩波动模型更强的预测能力;在高阶矩波动模型中包含杠杆效应项并不能提高模型的预测精度。最后提出了在金融风险管理、衍生产品定价等领域引入四阶矩波动模型的研究思路。     

Financial Risk Modelling and Econometric Inference

In finance, the explicit modelling of uncertainty takes on a particularly important role. The values of financial derivatives increase in the return volatility of the underlying security. This notion requires a concept of volatility and hence uncertainty. In addition, the choice between modelling in discrete and continuous time is not arbitrary, since it corresponds to a distinction between incomplete and complete markets, respectively, and this distinction matters for asset pricing, financial risk modelling, and inference. Risk and volatility are closely connected, and implied volatility, volatility forecasting, volatility in term structure models, stochastic volatility, and portfolio analysis are considered and related to a more general interplay between cross-sectional and dynamic aspects in finance. Stocks, bonds, and options are considered and placed in the context of efficiency and separation in inference.     

Analysis of VIX Markets with a Time-Spread Portfolio

This paper explores the relationship between option markets for the S&P500 (SPX) and Chicago Board Options Exchange’s CBOE’s Volatility Index (VIX). Results are obtained by using the so-called time-spread portfolio to replicate a future contract on the squared VIX. The time-spread portfolio is interesting because it provides a model-free link between derivative prices for SPX and VIX. Time spreads can be computed from SPX put options with different maturities, which results in a term structure for squared volatility. This term structure can be compared to the VIX-squared term structure that is backed-out from VIX call options. The time-spread portfolio is also used to measure volatility-of-volatility (vol-of-vol) and the volatility leverage effect. There may emerge small differences in these measurements, depending on whether time spreads are computed with options on SPX or options on VIX. A study of 2012 daily options data shows that vol-of-vol estimates utilizing SPX data will reflect the volatility leverage effect, whereas estimates that exclusively utilize VIX options will predominantly reflect the premia in the VIX-future term structure.     

上证综指的已实现波动率预测模型

采用上证综指2000-2008年的高频数据,在考察了中国股市已实现波动率的特征(即具有长记忆性、结构突变、不对称性和周内效应的特征并且结构突变只能部分解释已实现波动率的长记忆性)的基础上,构建了一个自适应的不对称性HAR-D-FIGARCH模型,并用于波动率的预测。模型的估计结果表明,与其他HAR模型相比,该模型对样本内数据的拟合效果最好。最后,通过SPA检验实证评价和比较了该模型与其他5种已实现波动率预测模型的样本外预测精度。结果发现,在各种损失函数下,该模型是预测中国股市已实现波动率精度最高的模型。     

Ornstein–Uhlenbeck processes in Hilbert space with non-Gaussian stochastic volatility

We propose a non-Gaussian operator-valued extension of the Barndorff-Nielsen and Shephard stochastic volatility dynamics, defined as the square-root of an operator-valued Ornstein–Uhlenbeck process with Lévy noise and bounded drift. We derive conditions for the positive definiteness of the Ornstein–Uhlenbeck process, where in particular we must restrict to operator-valued Lévy processes with “non-decreasing paths”. It turns out that the volatility model allows for an explicit calculation of its characteristic function, showing an affine structure. We introduce another Hilbert space-valued Ornstein–Uhlenbeck process with Wiener noise perturbed by this class of stochastic volatility dynamics. Under a strong commutativity condition between the covariance operator of the Wiener process and the stochastic volatility, we can derive an analytical expression for the characteristic functional of the Ornstein–Uhlenbeck process perturbed by stochastic volatility if the noises are independent. The case of operator-valued compound Poisson processes as driving noise in the volatility is discussed as a particular example of interest. We apply our results to futures prices in commodity markets, where we discuss our proposed stochastic volatility model in light of ambit fields.     

Calibrating the Black-Derman-Toy model: some theoretical results

The Black-Derman-Toy (BDT) model is a popular one-factor interest rate model that is widely used by practitioners. One of its advantages is that the model can be calibrated to both the current market term structure of interest rate and the current term structure of volatilities. The input term structure of volatility can be either the short term volatility or the yield volatility. Sandmann and Sondermann derived conditions for the calibration to be feasible when the conditional short rate volatility is used. In this paper conditions are investigated under which calibration to the yield volatility is feasible. Mathematical conditions for this to happen are derived. The restrictions in this case are more complicated than when the short rate volatilities are used since the calibration at each time step now involves the solution of two non-linear equations. The theoretical results are illustrated by showing numerically that in certain situations the calibration based on the yield volatility breaks down for apparently plausible inputs. In implementing the calibration from period n to period n + 1, the corresponding yield volatility has to lie within certain bounds. Under certain circumstances these bounds become very tight. For yield volatilities that violate these bounds, the computed short rates for the period (n, n + 1) either become negative or else explode and this feature corresponds to the economic intuition behind the breakdown.     

基于高频波动率模型与R-vine copula的行业资产组合风险测度研究

相较于低频波动率模型,高频波动率模型在单资产的波动和风险预测中均取得了更好效果,因此如何将高频波动率模型引入组合风险分析具有重要的理论和现实意义。本文以沪深300指数中的6种行业高频数据为例,运用滚动时间窗技术建立9类已实现波动率异质自回归(HAR-RV-type)模型刻画行业指数波动,同时使用R-vine copula模型描述行业资产间相依结构,进一步结合均值-CVaR模型优化行业资产组合投资比例,构建组合风险的预期损失模型,并通过返回测试比较不同风险模型的精度差异。研究结果表明:将HAR族高频波动率模型引入组合风险分析框架,能够有效预测行业资产组合风险状况;高频波动率预测的准确性将进而影响组合风险测度效果,跳跃、符号跳跃变差以及符号正向、负向跳跃变差均有助于提高行业组合风险的预测精度。