基于GARCH-GH模型的上证50ETF期权定价研究

上证50ETF期权是中国推出的首支股票期权.为描述上证50ETF收益率偏态、尖峰、时变波动率等特征,结合GARCH模型和广义双曲(Generalized Hyperbolic,GH)分布两方面的优势,建立GARCH-GH模型为上证50ETF期权定价.在等价鞅测度下,利用蒙特卡罗方法估计上证50ETF欧式认购期权价格.实证表明,相比较Black-Scholes模型和GARCH-Gaussian模型,GARCH-GH模型得到的结果更接近于上证50ETF期权的实际价格,其定价误差最小.     

基于随机波动率模型的上证50ETF期权定价研究

传统上,期权定价主要基于Black-Scholes (B-S)模型。但B-S模型不能描述时变波动率以及解释"波动率微笑"现象,导致期权定价存在较大的误差。随机波动率模型克服了B-S模型的这些缺陷,能够合理地刻画波动率动态性和波动率微笑。基于此,本文考虑随机波动率模型下的期权定价问题,并针对我国上证50ETF期权进行实证分析。为了解决定价模型的参数估计问题,采用上证50ETF及其期权价格数据,建立两步法对定价模型的参数进行估计。该估计方法保证了定价模型在客观与风险中性测度下的一致性。采用2016年1月到2017年10月的上证50ETF期权价格数据为研究样本,对随机波动率模型进行了实证检验。结果表明,无论是在样本内还是样本外,随机波动率模型相比传统的常数波动率B-S模型都能够获得明显更为精确和稳定的定价结果,B-S模型的定价误差总体偏大且呈现较高波动,凸显了随机波动率对于期权定价的重要性。另外,随机波动率模型对于短期实值期权的定价相比对于其它期权的定价要更精确。     

上证50ETF期权定价有效性的研究:基于B-S-M模型和蒙特卡罗模拟

上证50ETF期权作为中国资本市场上股票期权的第一个试点产品,其定价问题尤为重要。本文分别运用B-S-M期权定价模型和蒙特卡罗模拟方法对其定价进行实证研究,分析结果表明:1)IGARCH模型比传统的GARCH模型更能较好地拟合上证50ETF的波动率;2)当模拟次数为1000时,蒙特卡罗方法的效率一致地高于B-S-M模型,并且除了对偶变量技术的拟蒙特卡罗其他模型的精确度也都高于B-S-M模型;3)B-S-M模型和蒙特卡罗模拟方法都可以较为准确地、有效地模拟出上证50ETF期权价格。这些研究将为今后期权定价模型的发展和完善提供必要的参考和指引。     

基于最大熵和最小交叉熵方法的上证50ETF期权定价

基于最大熵方法和最小交叉熵方法,给出了根据期权价格推断标的资产价格分布的模型和已知先验信息下推断标的资产价格分布的模型,利用拉格朗日乘子法给出了模型的简化解,通过粒子群算法求出标的资产价格的密度函数,进而对上证50ETF期权进行定价比较.实证结果表明:基于最大熵方法推断的分布可以作为标的资产价格分布的较好估计;基于最小交叉熵方法推断的分布是在先验信息下标的资产价格分布的较好估计,两种方法适用于我国上证50ETF期权定价.     

双侧伽马期权定价与B-S模型的比较研究

本文首次运用双侧伽马分布对上证50ETF期权定价进行实证研究,并与经典的B-S模型进行比较。实证结果表明:采用双侧伽马模型来估算期权的理论价格,无论是在95%置信区间下还是在99%置信区间下,双侧伽马模型对于期权价格的测定都要优于B-S模型期权定价,因此,双侧伽马模型可以作为B-S模型的一种改进。     

分数布朗运动下带交易费用和红利的两值期权定价

本文研究了在分数布朗运动环境下带交易费用和红利的两值期权定价问题.在标的资产服从几何分数布朗运动的情况下,利用分数It公式和无风险套利原理建立了分数布朗运动环境下带交易费用和红利的两值期权的定价模型.再通过用偏微分方程的方法进行求解此定价模型,得到了在分数布朗运动下带交易费用和红利的两值期权定价公式.所得结果推广了已有结论.     

基于时间变换和分数型过程下的期权定价及模拟分析

由布朗运动驱动的期权定价模型是最为经典的模型,但该模型不能准确地描述资产价格的长相依性和短时间的不变性.本文提出了时间变换下的次分数布朗运动支付红利期权定价模型.首先,建立了次分数布朗运动扩散B-S模型,获得了带红利的欧式期权定价公式.其次,利用金融实际数据进行统计模拟,研究表明新模型能够反映金融资产真实值.     

时变混合分数布朗运动下带交易费用的亚式期权定价

考虑到经典的Black-Scholes(B-S)期权定价模型不能描述金融资产价格常值周期性、长相依性等特征,因此采用时变混合分数布朗运动描述金融资产价格的变动,并且对亚式期权定价时也考虑了交易费用.运用自融资Delta对冲策略得出了在离散情形下几何平均亚式看涨期权价格所满足的偏微分方程以及几何平均亚式看涨、看跌期权的定...     

分数布朗运动环境下的幂期权定价

在等价鞅测度下,研究标的资产价格服从几何分数布朗运动的幂期权看涨、看跌定价公式及其平价公式.并与基于标准布朗运动的幂期权定价公式进行比较分析,进一步论证布朗运动只是分数布朗运动的一种特例,可基于分数布朗运动对原有的期权定价模型进行推广.     

分数随机利率模型中的期权定价

本文研究分数随机利率模型中的期权定价问题.通过选取不同的资产作为计价单位及相应的测度交换,将经典模型中的测度变换方法推广到分数布朗运动市场环境,既丰富了分数期权定价的拟鞅方法,也得到了股票价格与利率分别服从几何分数布朗运动时的期权定价公式.     

一类多元回归模型参数的优于BLUE的估计

本文考虑多元线性回归模型i=1,2,B_i 未知在一定的条件下,得到参数的优于 BLUE 的估计。     

方差分析模型中参数的经验Bayes估计及其优良性问题

本文考虑单向分类的方差分析模型，构造了Ｐ′α的线性Ｂａｙｅｓ估计和经验Ｂａｙｅｓ（ＥＢ）估计，此处αａ×１是效应参数向量，Ｐａ×ｋ是常数矩阵．在较一般的条件下，基于均方误差矩阵准则和ＰｉｔｍａｎＣｌｏｓｅｎｅｓｓ准则，我们分别证明了ＥＢ估计优于最小二乘估计     

On a Problem of D. H. Lehmer

The main purpose of this paper is to use the Fourier expansion for character sums and the mean value theorem of Dirichlet L-functions to study the asymptotic property of the difference between a D. H. Lehmer number and its inverse modulo p （an odd prime）, A interesting mean square value formula is also given.     

离散时间马尔可夫跳变非线性系统H∞控制

讨论离散时间马尔可夫跳变非线性系统(MJNSs)的H∞控制。首先,本文采用一个马尔可夫跳变模糊系统(MJFS)来描述所研究的离散时间MJNS。然后,针对MJFS的跳变参数能够被在线实时检测和不能够被实时检测两种情况,分别给出了模式相关和模式无关的控制器设计方法。所得到的控制器能够保证闭环M JFS均方渐近稳定并且具有有限的L2增益。结果表明,控制器的设计可以转化为一组耦合的线性矩阵不等式求解的问题。     

Weighted Multivariate Mean Square Error for processes optimization: A case study on flux-cored arc welding for stainless steel claddings

A mathematical programming technique developed recently that optimizes multiple correlated characteristics is the Multivariate Mean Square Error (MMSE). The MMSE approach has obtained noteworthy results, by avoiding the production of inappropriate optimal points that can occur when a method fails to take into account a correlation structure. Where the MMSE approach is deficient, however, is in cases where the multiple correlated characteristics need to be optimized with varying degrees of importance. The MMSE approach, in treating all responses as having the same importance, is unable to attribute the desired weights. This paper thus introduces a strategy that weights the responses in the MMSE approach. The method, called the Weighted Multivariate Mean Square Error (WMMSE), utilizes a weighting procedure that integrates Principal Component Analysis (PCA) and Response Surface Methodology (RSM). In doing so, WMMSE obtains uncorrelated weighted objective functions from the original responses. After being mathematically programmed, these functions are optimized by employing optimization algorithms. We applied WMMSE to optimize a stainless steel cladding application executed via the flux-cored arc welding (FCAW) process. Four input parameters and eight response variables were considered. Stainless steel cladding, which carries potential benefits for a variety of industries, takes low cost materials and deposits over their surfaces materials having anti-corrosive properties. Optimal results were confirmed, which ensured the deposition of claddings with defect-free beads exhibiting the desired geometry and demonstrating good productivity indexes.     

不确定离散时间马尔可夫跳变模糊系统鲁棒H∞控制

讨论不确定离散时间马尔可夫跳变模糊系统(MJFS)的鲁棒H∞控制。首先,本文给出了能够保证系统鲁棒稳定且具有H∞鲁棒度的一个充分条件。然后采用并行分布补偿算法,将系统鲁棒H∞控制控制器的设计转化成为了一组线性矩阵不等式的求解问题,方便使用Matlab求解。最后的仿真结果表明,本文所提出的方法是有效的。     

VARIATION IN THE MEAN SQUARED ERROR OF ESTIMATES DUE TO FUZZINESS IN THE INFORMATION SYSTEM

In the general problem of Parametric Point Estimation the Mean Squared Error often appears as a useful measure of goodness or closeness of estimates. Nevertheless, in very rare cases an estimator with smallest Mean Squared Error exists, but Statistical Inference provides a variety of methods to find estimates. that are usually characterized by a small Mean Squared Error.When the observation of outcomes from the probabilistic information system or experiment concerning the estimation problem involves fuzzy imprecision, so that the observable events are described by means of fuzzy events on the sample space, the use of Zadeh's probabilistic definition allows us to immediately extend the Mean Squared Error.In the present paper we are going to verify that the presence of fuzziness in experimental data entails a variation in that measure of goodnesss of estimation. On the basis of the last assertion the problem of selecting the suitable sample size, in order to remove the variation in the Mean Squared Error due to fuzziness or to estimate the parameter with a specified degree of precision, will be then discussed.     

二阶矩模糊随机过程的均方收敛性

给出二阶矩模糊随机过程及其均方收敛的定义,证明二阶矩模糊随机过程均方收敛的栖西准则,讨论二阶矩模糊随机过程的均方收敛的性质。     

Multidirectional Mean Value Inequalities in Quasidifferential Calculus

In the current paper, a Clarke–Ledyaev type mean value inequality is proved for semicontinuous functions defined in a Banach space that are quasidifferentiable in the sense of Demyanov–Rubinov. A stronger variant valid under compactness assumption in separable spaces and extensions for functions with semicontinuous Dini derivatives in locally uniformly convex Banach spaces and with merely bounded Dini derivatives are then established. Subsequently, applications of these mean value inequalities to solvability of nonsmooth parametric equations and to the estimation of local and global Hoffman error bound for inequalities are investigated via a decrease principle.     

A low order anisotropic nonconforming characteristic finite element method for a convection-dominated transport problem

A low order anisotropic nonconforming rectangular finite element method for the convection-diffusion problem with a modified characteristic finite element scheme is studied in this paper. The O(h²) order error estimate in L²-norm with respect to the space, one order higher than the expanded characteristic-mixed finite element scheme with order O(h), and the same as the conforming case for a modified characteristic finite element scheme under regular meshes, is obtained by use of some distinct properties of the interpolation operator and the mean value technique, instead of the so-called elliptic projection, which is an indispensable tool in the convergence analysis of the previous literature. Lastly, some numerical results of the element are provided to verify our theoretical analysis.