香港银行间同业拆借利率的非参数统计分析

首次利用短期利率模型,分析香港银行同业拆借利率(Hibor),揭示了最近十年内香港银行同业拆借利率的基本特征.初步分析表明,Hibor数据的平稳性不能保证,因此采用了非参数统计方法.利用bandi文章中的方法,给出了函数的漂移项和扩散项的非参数估计,同时还得到了过程的局部时估计.通过实证分析,发现香港银行间同业拆借利率在2006至2015年间,以2009年为界,前后两个时间段的数据表现出不同的特征,样本数据的局部时函数也表现为双峰分布.     

短期Shibor跳跃行为的利率模型解释

上海银行间同业拆借利率(Shibor)自运行以来,短期Shibor品种波动异常频繁和剧烈.本文通过对短期Shibor数据的描述和相关统计检验,构建了一个适合其动态特征的ARCH跳跃扩散模型,并通过实证表明,跳跃行为和ARCH效应是描述短期Shibor波动的主要因素.随后结合Shibor运行的宏微观背景,在该模型框架下进行分析,得到大型IPO和未预期到的货币政策调整是导致Shibor跳跃行为的两个主要原因.     

人民币短期利率行为研究方法的一个改进——双指数Jump-GARCH-Vasicek模型的构建与应用

受货币政策调控频率提升及大型新股申购等因素的影响,近年来人民币短期利率表现出明显的跳跃行为。为了更准确地描述利率跳跃行为,本文通过假设跳跃幅度服从双指数分布构建一个能刻画短期利率波动聚类、均值回复和跳跃行为的双指数Jump-GARCH-Vasicek模型。利用人民币短期利率数据,将双指数Jump-GARCH-Vasicek模型与Vasicek模型、GARCH-Vasicek模型、正态Jump-Vasicek模型、双指数Jump-Vasicek模型、正态Jump-GARCH-Vasicek模型进行实证对比分析。研究结果表明,人民币短期利率确实存在GARCH效应、均值回复和跳跃行为,且双指数Jump-GARCH-Vasicek模型较其它模型能更好地刻画人民币短期利率的跳跃行为。     

中国债券市场动态利率模型及其实证检验

为了对中国债券市场动态利率期限结构进行深入的研究,本文基于状态空间模型和卡尔曼滤波技术构建了中国债券市场动态利率模型。本文模型根据数据的可观测结构进行建模,通过迭代计算寻找不可观测状态变量的最优估计值和隐含参数,很好地解决了传统计量方法中因为变量不可观测而无法获得真实数据所带来的研究困难。同时通过模型有效性的模拟实验和中国债券市场同业拆借利率的实证研究,证明了模型对利率期限结构在一段时间内的动态变化估计结果准确,在建模样本期内利率的动态变化能够得到有效的分析和预测。本文的研究为中国债券市场动态利率管理和定价问题提供了新的思路和可能的解决渠道。     

我国短期利率行为特征-基于带跳和异方差的CKLS利率模型研究

选取同行拆借IBO007利率数据,采用拟似然函数估计构建的CKLS类四个模型,研究结果表明:含有跳和异方差的CKLSGJ模型是此类模型中最佳的短期利率模型,模型能恰当的解释我国短期利率均值回复性、水平效应及跳跃行为.蒙特卡洛模拟结果表明:模型能较好的拟合数据,有很强的预测能力.     

经济政策不确定性与短期利率波动——基于BHK-L-MIDAS模型的实证研究

本文在BHK模型的基础上，考虑短期利率波动杠杆效应和EPU对短期利率波动的影响，构建了一个包含杠杆效应和EPU的混频短期利率模型，即BHK-L-MIDAS模型对短期利率波动进行建模与预测。采用上海银行间同业拆借利率(SHIBOR)和中国EPU指数数据对构建的BHK-L-MIDAS模型进行实证分析，结果表明：短期利率波动存在“反向杠杆效应”;EPU对短期利率波动具有显著负向的影响；BHK-L-MIDAS模型相较于竞争模型(BHK和BHK-MIDAS模型)获得了更好的样本内数据拟合效果。基于三种损失函数以及模型置信集(MCS)检验对模型样本外短期利率波动预测能力的分析表明：BHK-L-MIDAS模型相比BHK模型和BHK-MIDAS模型具有更高的样本外预测精度，且BHK-L-MIDAS模型在不同预测窗口表现出的预测能力具有稳健性。最后，VaR分析表明BHK-L-MIDAS模型在短期利率市场风险度量方面的经济价值。     

中国银行间拆借利率扩散模型的极大拟似然估计

本文用极大拟似然估计法估计了中国银行间市场七天拆借利率扩散模型的参数。并用自助法对众多不同的模型进行了广义拟似然比检验。结论表明:中国货币市场利率具有均值回复效应:利率敏感系数γ值为1.421265,对利率水平具有较高敏感性。     

人民币汇率波动与我国房价关系的实证分析

分析了汇率影响房价的机制,利用人民币实际有效汇率、房地产价格指数和银行同业拆借利率共30组数据(2005,07～2007,12)建立了向量自回归模型(VAR),并使用协整、Granger因果检验,脉冲响应分析对人民币汇率波动与我国房地产价格之间的关系进行实证检验.研究结果表明,人民币实际有效汇率对房地产价格产生正向影响,人民币升值是引起房价上涨的格兰杰原因.在现阶段,控制因人民币升值而进入中国的境外资金过度流入房地产市场,有利于保持我国房地产价格稳定.     

基于变差理论的利率基准性已实现波动分析

从利率波动状况的角度,利用变差理论,对我国的三种利率体系短期利率的波动状况进行研究并分离出利率的跳跃过程。结果表明相对Libor美元报价利率的波动性,我国的利率短期品种波动性表现较为剧烈,跳跃现象频繁,这三种利率体系尚不能完全独立地作为我国货币市场的基准利率。但作为定价基准,回购定盘利率更适合做隔夜和一周的参考利率,Shibor一月期限的拆借利率要优于Chibor的一月拆借利率。本文结论有利于市场主体选择金融资产收益率的定价标准以及衡量国内利率体系的合理性。     

可转换债券:参数估计与定价实证

金融产品的定价,是金融工程研究的核心问题之一,同样可转换债券的定价也引起国内外学者们的关注.本文试图借鉴国内外研究成果,在分析股价及利率特性的基础上,运用推导出基于股价和利率的双因素定价模型;从中国实情出发,运用广义自回归条件异方差模型(简称GARCH)得出长期波动率,通过将可转债条款转化为边界终值条件并利用数值方法对可转债定价.     

Estimates of stability of characterization of additive types of distributions

An estimate of stability of characterization of distribution types is obtained for the case of additive types. Under some conditions, the estimate has the order ε^1/3L(ε), where L(ε) is a slowly varying function. Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I.     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

一类完全正则半群簇子簇格的性质

本文研究了完全正则半群簇的子簇格［Ｖ＋∩ＰＶ，Ｖ＋∩ＰＶ］的某些格运算性质，我们证明了簇Ｖ＋∩ＰＶ可分解为Ｖ与Ｖ＋∩ＰＶ的并；对任意完全正则半群簇Ｗ，有Ｗ∩（Ｖ∨Ｖ＋∩ＰＶ）＝（Ｗ∩Ｖ）∨（Ｗ∩Ｖ＋∩ＰＶ）．特别地，我们得到了等式Ｖ＋∩ＰＶ＝Ｖ成立的若干条件．     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

Distribution of types of symmetry of tensors of high degree

The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986.     

Preservation of equivalence of derivations under reduction of depth of formulas

In this paper we consider derivations in the (&, )-fragment of the intuitionistic propositional calculus. As is known, replacement of any occurrence of a formula [F] in a sequent S by an occurrence of the formula [p], where p is a new propositional variable, with the simultaneous addition to the antecedent of the formula F p or p F depending on the sign of the occurrence of F in S, leaves the derivability unchanged. We give a proof of the fact that the natural extension of this transformation to derivations preserves the relation of equivalence of derivations, i.e., transformed derivations are equivalent if and only if the originals are equivalent. (Derivations are considered equivalent if certain of their normal forms coincide, or, what is the same, if their deductive terms coincide.) It is proved that by the iteration of this transformation, each derivation of an arbitrary sequent S can be transformed into a derivation of a sequent S, depending only on S, whose succedent is a variable, and in the antecedent there occur only formulas of the form a,a & b, a b,,(a b) c, a & b c, a (b & c), wherea, b, c are variables. Here if S is balanced, then S is also balanced. (A sequent is called balanced if each variable occurs in it no more than twice.) The familiar correspondence between certain concepts of the theory of categories and concepts of the theory of proofs allows one to assert that there has been constructed a univalent functor, mapping a free Cartesian closed category into itself.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 88, pp. 197–207, 1979.     

Estimate of growth of Lebesgue functions of linear methods of summation

Sufficient conditions are obtained in terms of matrix elements for the boundedness of Lebesgue functions of linear methods of summation of expansions in orthogonal systems of polynomial type.Translated from Matematicheskie Zametki, Vol. 6, No. 3, pp. 277–286, September, 1969.