随机波动率模型下的VIX期权定价

本文主要有两部分:第1部分找到一个拟合VIX指数能力较优的随机波动率模型;第2部分是在较优模型下讨论VIX指数期权定价问题.其中第1部分首先利用非参数方法估计随机波动率模型的漂移项和扩散项,然后在此基础上对七个经典随机波动率模型进行拟合和比较.第2部分在较优模型基础上加上跳跃,讨论期权定价的PDE和解析解.     

部分线性混合效应模型中方差分量的稳健估计

部分线性混合效应模型中方差分量是我们感兴趣的参数, 文献中已经给出许多估计方法. 但是其中很多方法都可以归结为广义估计方程方法(GEE), 如: 最大似然估计(MLE), 约束最大似然估计(REMLE)等, 而GEE方法对异常点很敏感. 本文提出一组关于部分线性混合效应模型(PLMM)中均值和方差分量的稳健估计方程, 对均值和方差分量同时进行稳健估计; 并进行了随机模拟考察所提出稳健估计的有效性, 最后通过两个实例, 说明了所提方法的可行性.     

基于权函数的GARCH模型稳健建模及实证分析

异常值的存在会对时间序列波动率模型的识别及参数估计会产生重要影响,采用Tukey双权法权函数对被拟合相关序列模型的残差进行变换,再将变换后的残差序列对波动率模型进行稳健识别及建模,模拟及实证分析表明稳健识别及估计方法具有很好的耐抗性,而且能更好的捕捉到资产收益率的波动性.     

探索加密货币波动率预测中的模型不确定性问题:log转换、时区采样以及模型设定

文章全面地比较了一系列模型在预测加密货币波动率时的表现.结果发现,粗糙波动率模型在预测多期样本外的波动率时表现更加稳健和可靠,而异质自回归(HAR)模型相对较弱,但经过log转换后的HAR模型在预测上则表现更优.此外,考虑到加密货币的特点,选取合适的时区划分依据也非常重要,因为不同的时区可能对加密货币市场的波动率产生影响.研究还引入了最小二乘模型平均法来应对波动率建模中的模型不确定性.结果表明,模型平均方法在加密货币市场波动率预测中相比其他方法具有优越性,能够平衡不同模型之间的优缺点,提高预测的可信度和稳定性,对于预测市场的波动性是非常有效的.文章研究指出,在选择合适的波动率模型时需要综合考虑加密货币波动率的特性和历史表现,并且在应用模型时需要注意其在不同数据集和预测目标下的表现,避免盲目使用导致预测效果的不确定性.     

稳健AR模型的构建及比较研究

时间序列自回归AR模型在建模过程中易受离群值的影响,导致计算结果与实际不相符.针对这一现象,将Hampel权函数运用于自相关函数中,从而构建出自回归AR模型的稳健估计算法,以克服离群值的影响.并对此方法进行了模拟和实证分析,模拟和实证分析均表明:当时序数据中不存在离群值时,传统估计方法与稳健估计方法得到的结果基本保持一致;当数据中存在离群值时,运用传统估计方法得到的结果出现较大变化,而运用稳健估计方法得到的结果基本不变.这说明相对于传统估计方法,稳健估计方法能有效抵抗离群值的影响,具有良好的抗干扰性和高抗差性.     

宏观经济对股市波动的影响——基于GARCH-MIDAS-RTSRV模型的证据

本文对GARCH-MIDAS模型进行了拓展。首先,在估计GARCH-MIDAS模型的长期波动成分时,采用同时考虑噪声和跳跃影响的稳健双频已实现波动估计量RTSRV来代替传统的已实现波动估计量RV。其次,选取了经济变量并从中提取出主成分,从其水平值和波动率两个层面研究不同主成分对股市波动的影响。研究发现：本文构造的GARCH-MIDAS-RTSRV模型优于传统的GARCH-MIDAS模型,其预测精度更高并且可使投资者获得更高的经济价值;经济变量的主成分和已实现波动率均对股市的波动有显著的影响,并且相较于其水平值,波动率对股市波动的影响更为显著。     

基于Walsh平均的非参数回归模型的稳健估计

由于非参数回归模型复杂灵活,被广泛应用。在众多估计方法中,最小二乘法最为常用,一般情况下具有良好的性质,但在处理厚尾分布及异常点时表现的不够稳健。本文针对此,提出了基于Walsh平均的稳健样条估计。我们理论地推导了估计结果的相合性和渐近正态性;并与多项式样条回归做比较。计算得Walsh平均的样条估计相对于多项式样条回归的渐近相对效率与Wilcoxon符号秩检验相对于t-检验的渐近相对效率是一样的。在正态情形下我们的方法与多项式样条回归差不多,在非正态情形下,我们的方法表现更为稳健,效率明显优于多项式样条回归。     

稳健的模糊回归区间分析

由于传统的回归分析易受到异常值的影响。针对输入变量为实数,输出变量和输入参数为模糊数的情况,给出了一种稳健的模糊回归区间预测模型和算法。该模型基于输出变量的隶属度函数为目标函数,以估计的区间为约束条件。给出的算法具有较强的稳健性,利用该算法估计的区间几乎不受异常值的影响。最后通过一个数值算例,与其他模型算法对比分析,验证了该模型和算法的有效性和稳健性。     

基于跳-扩散模型的股票挂钩型理财产品的资产定价

本文在假定股票价格服从跳-扩散过程的基础上,研究两种常见的股票挂钩型理财产品的资产定价问题.首先,基于异常值检测方法对跳-扩散模型的参数进行估计,基于矩估计方法对几何布朗运动模型的参数进行估计,并对参数估计的有效性进行评估;然后,依据参数估计的结果对保本型理财产品和阈值型理财产品分别定价,并分析跳对产品价格的影响.对于本文涉及的保本型理财产品和阈值型理财产品,数值模拟发现:含跳过程的模型更能描述原始股价的波动情况,且股票价格服从跳-扩散模型时,两种理财产品的价格均高于股票价格服从几何布朗运动时的价格,从而说明跳过程所描述的这类事件会影响股票价格,并对理财产品的价格产生显著影响.因此,本文对含跳过程股票挂钩型理财产品的定价研究具有一定的现实意义.     

有调节的中介潜变量的循环效应模型

从解决大学生网络成瘾和抑郁相互影响关系的研究出发,构建了有调节的中介潜变量的循环效应模型.为对模型变量进行效应大小的分析和比较,推导出模型参数的标准化估计.运用我们提出的基于配方约束的潜变量回归的确定性线性算法来计算潜变量的值,避免了交互潜变量计算时观测变量的配对问题.对模型参数的OLS估计可能不具有一致性和无偏性进行了证明,并给出了解决问题的相应算法.总结出模型的算法步骤和变量的效应检验步骤.最后进行了数值模拟,验证了模型的合理性.     

Some closed form robust moment‐based estimators for the MEM(1,1)

In this paper, we extend the closed form moment estimator (ordinary MCFE) for the autoregressive conditional duration model given by Lu et al (2016) and propose some closed form robust moment‐based estimators for the multiplicative error model to deal with the additive and innovational outliers. The robustification of the closed form estimator is done by replacing the sample mean and sample autocorrelation with some robust estimators. These estimators are more robust than the quasi‐maximum likelihood estimator (QMLE) often used to estimate this model, and they are easy to implement and do not require the use of any numerical optimization procedure and the choice of initial value. The performance of our proposal in estimating the parameters and forecasting conditional mean μ_t of the MEM(1,1) process is compared with the proposals existing in the literature via Monte Carlo experiments, and the results of these experiments show that our proposal outperforms the ordinary MCFE, QMLE, and least absolute deviation estimator in the presence of outliers in general. Finally, we fit the price durations of IBM stock with the robust closed form estimators and the benchmarks and analyze their performances in estimating model parameters and forecasting the irregularly spaced intraday Value at Risk.     

GARCH模型估计方法选择及对上证指数的应用

本文介绍了对ARCH/GARCH模型的两种估计方法:准极大似然估计和极小绝对偏差估计,并提出了一种基于自助法(Bootstrap)对估计方法的选择。在厚尾程度不同的情况下进行了模拟分析,表明对于一个具体的数据,该选择法能够自动选择较优的估计方法。并用该方法对上海证券交易所A股和B股的股价指数进行了分析,印证了上海股市B股收益率的尾部厚于A股收益率尾部。     

Robust autoregressive estimates using quadratic programming

The robust estimation of the autoregressive parameters is formulated in terms of the quadratic programming problem. This article's main contribution is to present an estimator that down weights both types of outliers in time series and improves the forecasting results. New robust estimates are yielded, by combining optimally two weight functions suitable for Innovation and Additive outliers in time series. The technique which is developed here is based on an approach of mathematical programming applications to I_p-approximation. The behavior of the estimators are illustrated numerically, under the additive outlier generating model. Monte Carlo results show that the proposed estimators compared favorably with respect to M-estimators and bounded influence estimators. Based on these results we conclude that one can improve the robust properties of AR(p) estimators using quadratic programming.     

Robust estimation in generalized semiparametric mixed models for longitudinal data

In this paper, we consider robust generalized estimating equations for the analysis of semiparametric generalized partial linear mixed models (GPLMMs) for longitudinal data. We approximate the non-parametric function in the GPLMM by a regression spline, and make use of bounded scores and leverage-based weights in the estimating equation to achieve robustness against outliers and influential data points, respectively. Under some regularity conditions, the asymptotic properties of the robust estimators are investigated. To avoid the computational problems involving high-dimensional integrals in our estimators, we adopt a robust Monte Carlo Newton-Raphson (RMCNR) algorithm for fitting GPLMMs. Small simulations are carried out to study the behavior of the robust estimates in the presence of outliers, and these estimates are also compared to their corresponding non-robust estimates. The proposed robust method is illustrated in the analysis of two real data sets.     

稳健残差控制图的构建及在金融时序中的应用

对于呈现自相关和波动族聚性并存的受控过程,通常采用残差控制图对其进行监控。但异常点的存在会对自相关或波动族聚性模型的拟合产生重要影响,使得基于该模型的残差并非独立同分布导致常规残差控制图监控失效。为解决这类问题,本文提出稳健残差控制图。即建立稳健的ARMA模型解决自相关问题从而得到无自相关的残差序列,用稳健的GARCH模型来构建控制图的上下限。模拟和实证研究表明,本文提出的稳健残差控制图具有很好的抗异常点能力并能更好的对金融时间序列的异常现象进行监控。     

高频视角下中国股市动态VaR预测模型研究

如何充分挖掘交易数据中有价值的信息对金融风险管理极其重要,现有研究中基于低频波动模型的风险测度方法几乎已经做到了极致,而能达到的预测效果却并不稳健,对高频波动模型的研究相对比较匮乏。那么高频模型能否从高频数据中挖掘出更有价值的信息以便用于风险管理之中呢？本研究通过建立12个低频和9个高频波动模型对上证综指进行样本外动态VaR的滚动预测发现,高频模型相对于低频模型具有更好的稳定性,并且在多数情况下高频模型优于低频模型;多头与空头的风险预测效果具有显著差异,多头风险在高风险情况下高频模型表现出色,低风险情况下并不理想,空头风险则在所有情况下都表现较好。     

Robustness of reweighted Least Squares Kernel Based Regression

Kernel Based Regression (KBR) minimizes a convex risk over a possibly infinite dimensional reproducing kernel Hilbert space. Recently, it was shown that KBR with a least squares loss function may have some undesirable properties from a robustness point of view: even very small amounts of outliers can dramatically affect the estimates. KBR with other loss functions is more robust, but often gives rise to more complicated computations (e.g. for Huber or logistic losses). In classical statistics robustness is often improved by reweighting the original estimate. In this paper we provide a theoretical framework for reweighted Least Squares KBR (LS-KBR) and analyze its robustness. Some important differences are found with respect to linear regression, indicating that LS-KBR with a bounded kernel is much more suited for reweighting. In two special cases our results can be translated into practical guidelines for a good choice of weights, providing robustness as well as fast convergence. In particular a logistic weight function seems an appropriate choice, not only to downweight outliers, but also to improve performance at heavy tailed distributions. For the latter some heuristic arguments are given comparing concepts from robustness and stability.     

Robust algorithms for multiphase regression models

This paper proposes a robust procedure for solving multiphase regression problems that is efficient enough to deal with data contaminated by atypical observations due to measurement errors or those drawn from heavy-tailed distributions. Incorporating the expectation and maximization algorithm with the M-estimation technique, we simultaneously derive robust estimates of the change-points and regression parameters, yet as the proposed method is still not resistant to high leverage outliers we further suggest a modified version by first moderately trimming those outliers and then implementing the new procedure for the trimmed data. This study sets up two robust algorithms using the Huber loss function and Tukey's biweight function to respectively replace the least squares criterion in the normality-based expectation and maximization algorithm, illustrating the effectiveness and superiority of the proposed algorithms through extensive simulations and sensitivity analyses. Experimental results show the ability of the proposed method to withstand outliers and heavy-tailed distributions. Moreover, as resistance to high leverage outliers is particularly important due to their devastating effect on fitting a regression model to data, various real-world applications show the practicability of this approach.     

Asymptotic inference of unstable periodic ARCH processes

This paper studies asymptotic properties of the quasi maximum likelihood and weighted least squares estimates (QMLE and WLSE) of the conditional variance slope parameters of a strictly unstable ARCH model with periodically time varying coefficients (PARCH in short). The model is strictly unstable in the sense that its parameters lie outside the strict periodic stationarity domain and its boundary. Obtained from the regression form of the PARCH, the WLSE is a variant of the least squares method weighted by the square of the conditional variance evaluated at any fixed value in the parameter space. In calculating the QMLE and WLSE, the conditional variance intercepts are set to any arbitrary values not necessarily the true ones. The theoretical finding is that the QMLE and WLSE are consistent and asymptotically Gaussian with the same asymptotic variance irrespective of the fixed conditional variance intercepts and the weighting parameters. So because of its numerical complexity, the QMLE may be dropped in favor of the WLSE which enjoys closed form.     

Quasi-maximum likelihood estimation for multiple volatility shifts

We propose the Gaussian quasi-maximum likelihood estimator (QMLE) to detect and locate multiple volatility shifts. Our Gaussian QMLE is shown to be consistent under suitable conditions and the rate of convergence is provided. It is also shown that the binary segmentation procedure provides a consistent estimation for the number of volatility shifts.