基于修正的已实现阈值幂变差的股市跳跃波动行为研究

基于非参数统计方法,利用考虑金融资产价格跳跃和杠杆效应的时点波动估计方法修正已实现阈值幂变差,构造甄别跳跃的检验统计量,对金融资产价格中的随机波动、有限活跃跳跃和无限活跃跳跃等问题进行综合研究。为同时吸收波动率的异方差集聚效应和收益率的非对称效应,对原有的已实现波动率异质自回归预测模型进行拓展,将非对称的异质性自回归模型的误差项设定为GARCH模型,以考察跳跃波动序列与连续波动序列之间的复杂关系。利用沪深股指高频数据进行实证研究,包括进行跳跃识别,跳跃活动程度检验和波动率预测效果对比。研究结果表明,沪深股市同时存在布朗运动成分、有限活跃跳跃和无限活跃跳跃成分,其中连续路径方差占主体。同时,收益和波动间的杠杆效应显著,无论短期还是长期,连续波动和跳跃波动对波动率的预测均具有显著影响,同时考虑股价的跳跃、波动和杠杆效应因素有助于更准确地刻画资产价格动态过程。     

Option pricing under jump-diffusion models with mean-reverting bivariate jumps

We propose a jump-diffusion model where the bivariate jumps are serially correlated with a mean-reverting structure. Mathematical analysis of the jump accumulation process is given, and the European call option price is derived in analytical form. The model and analysis are further extended to allow for more general jump sizes. Numerical examples are provided to investigate the effects of mean-reversion in jumps on the risk-neutral return distributions, option prices, hedging parameters, and implied volatility smiles.     

Determination of jumps of distributions by differentiated means

Differentiated means are defined in order to find formulas for jumps of distributions. We analyze two types of jumps occurring in the notions of distributional jump behavior and symmetric jump behavior. We start by defining what we call Riesz differentiated means for numerical series, then the differentiated means are extended to distributional evaluations for the Schwartz class of tempered distributions. The jumps of tempered distributions are completely determined by the differentiated means of the Fourier transform. We also find formulas for the jumps in terms of the asymptotic behavior of partial derivatives of harmonic representations and harmonic conjugate functions. Applications to Fourier series are given. The second author gratefully acknowledges support by the Louisiana State Board of Regents grant LEQSF(2005-2007)-ENH-TR-21.     

The structure of evolutional jumps in reversible systems

A general theory for jump structures in reversible symmetric systems is developed. It is established that, as in systems with dissipation [1–3], the type of jump structure depends on the number of intersections of the dispersion curve and the straight line corresponding to the jump velocity, while jumps for which a structure exists turn out to be at the same time evolutional jumps. The theory is applicable in cases when the dispersive properties of the medium prevail over its dissipative properties.     

ENO Reconstruction and ENO Interpolation Are Stable

We prove that the ENO reconstruction and ENO interpolation procedures are stable in the sense that the jump of the reconstructed ENO point values at each cell interface has the same sign as the jump of the underlying cell averages across that interface. Moreover, we prove that the size of these jumps after reconstruction relative to the jump of the underlying cell averages is bounded. Similar sign properties and the boundedness of the jumps hold for the ENO interpolation procedure. These estimates, which are shown to hold for ENO reconstruction and interpolation of arbitrary order of accuracy and on nonuniform meshes, indicate a remarkable rigidity of the piecewise polynomial ENO procedure.     

资产价格中跳的检验与度量

分离估计归因于跳部分和连续部分对资产定价是非常重要的.由于市场信息的流入,前者通常比后者缺少可预测性.到目前为此,小波方法对于发现跳点和估计跳大小是有力的,正如王亚珍[1].但是在一些程度上,在点估计方面不能准确地对跳的位置和大小进行估计.本文中,我们提出了改进方法去估计已实现方差,从而新的估计量被用于在不同的取样策略...     

沪深300指数日内跳的Hausman检验

本文采用半鞅过程的双重次方变差和多重次方变差构造的跳检验统计量,对沪深300指数进行日内跳检验。检验结果表明,沪深300指数多于1/3的交易日有跳发生,跳发生的概率在不同交易时段并不均匀,并表现出一定的持续性。计算结果表明,跳二次变差在二次变差中占的比例高达32.48%,是二次变差的重要组成部分。     

The Gumbel test and jumps in the volatility process

In the framework of jump detection in stochastic volatility models the Gumbel test based on extreme value theory has recently been introduced. Compared to other jump tests it possesses the advantages that the direction and location of jumps may also be detected. Furthermore, compared to the Barndorff–Nielsen and Shephard test based on bipower variation the Gumbel test possesses a larger power. However, so far one assumption was that the volatility process is Hölder continuous, though there is empirical evidence for jumps in the volatility as well. In this paper we derive that the Gumbel test still works under the setting of finitely many jumps not exceeding a certain size. This maximal jump size depends on the relative sampling frequencies involved in the definition of the test statistics. Furthermore, we show that the given bound on the jump size is sharp and investigate the details of the phase transition at this critical bound.     

Black-Scholes期权定价公式推广

在Black-Scholes期权定价模型的基础上,进一步考虑标的资产受多个跳跃源影响的情况,用含有多维Poisson过程的Ito-Skorohod随机微分方程描述标的资产价格的动态运动,应用等价鞅测度变换方法导出一般形式的欧式期权定价公式,并讨论了利率,波动率不是常数情况下的拓广形式.     

A jump discontinuity of compressible viscous flows grazing a non-convex corner

We show existence and regularity of solution for the compressible viscous steady state Navier–Stokes system on a polygon having a grazing corner and that the density has a jump discontinuity across a curve inside the domain. There are corresponding jumps in derivatives of the velocity. The solution comes from a well-posed boundary value problem on a polygonal domain with a non-convex corner. A formula for the decay of the jump is given. The decay formula suggests that density jumps can occur in a compressible flow with a non-vanishing viscosity.     

双跳跃仿射扩散模型的几何平均型水平重置期权定价

在资产收益率及其波动率均满足随机跳跃且具有跳跃相关性的仿射扩散模型下,用广义双指数分布和伽玛分布分别刻画非对称性收益率及其波动率的跳跃波动变化,研究了具有几何平均特征的水平重置期权定价问题.通过Girsanov测度变换和多维Fourier逆变换方法,给出了此类重置期权定价的解析公式.最后,通过数值实例着重分析了联合跳跃...     

An Optimal Algorithm to Find the Jump Number of Partially Ordered Sets

The jump number of a partially ordered set (poset) P isthe minimum number of incomparable adjacent pairs (jumps) in some linearextension of P. The problem of finding a linear extension of Pwith minimum number of jumps (jump number problem) is known to beNP-hard in general and, at the best of our knowledge, no exactalgorithm for general posets has been developed. In this paper, wegive examples of applications of this problem and propose for thegeneral case a new heuristic algorithm and an exactalgorithm. Performances of both algorithms are experimentallyevaluated on a set of randomly generated test problems.     

Detection of the jump points of a heteroscedastic regression model by wavelets

1. IntroductionDetection of jump points often arises in many practical problems such as signal analysis,.... fimage processing, seismic exploratioll and phonetic identification. FOr examPle, financialeconollilsts often wad to know if abrupt changes occur in an exchange rate series sincethese changes edicted, are affecting or will affect fin-ancial market; engineers concern abolltwhether there exist jumps in a seismic signal in oil exploration bacause these jumps maypredict that there exists br…     

Mean first passage times of two-dimensional processes with jumps

In this paper, we incorporate a jump component into the model based on a two-dimensional degenerate diffusion process for the remaining lifetime of machines in the recent paper [Lefebvre, M., 2010. Mean first-passage time to zero for wear processes. Stochastic Models 26, 46-53] by the second author. We calculate explicitly the expected value of first passage times associated to the two-dimensional process when the jump component is taken to be a compound Poisson process with exponential jumps and random proportion of jumps.     

Genetic Algorithm for the Jump Number Scheduling Problem

This paper introduces genetic algorithms for the jump number scheduling problem. Given a set of tasks subject to precedence constraints, the problem is to construct a schedule to minimize the number of jumps. We show that genetic algorithms outperform the previously known Knuth and Szwarcfiter's exhaustive search algorithm when applied to some classes of orders in which no polynomial time algorithms exist in solving the jump number problem. Values for various parameters of genetic jump number algorithms are tested and results are discussed.     

Estimating functions for jump–diffusions

Asymptotic theory for approximate martingale estimating functions is generalised to diffusions with finite-activity jumps, when the sampling frequency and terminal sampling time go to infinity. Rate-optimality and efficiency are of particular concern. Under mild assumptions, it is shown that estimators of drift, diffusion, and jump parameters are consistent and asymptotically normal, as well as rate-optimal for the drift and jump parameters. Additional conditions are derived, which ensure rate-optimality for the diffusion parameter as well as efficiency for all parameters. The findings indicate a potentially fruitful direction for the further development of estimation for jump–diffusions.     

国际油价波动跳跃性特征的实证分析

根据国际油价波动中存在异常跳跃的情况,本文运用EGARCH-Jump模型对国际油价波动的跳跃性特征进行了实证分析。结果表明,加入跳跃因素的模型减缓了国际油价波动的持续性,同时杠杆效应消失,表明跳跃性因素是国际油价波动的影响因素之一,也证实了国际油价波动的跳跃性特征是国际石油市场产生杠杆效应的原因。但从长期来看,跳跃性因素对国际油价波动的扰动影响并不大,国际油价的波动仍主要受正常信息的影响。总体上,EGARCH-Jump模型比普通GARCH族模型能更好地捕捉国际油价波动的动态性特征。     

On finding the jump number of a partial orber by substitution decomposition

Consider the linear extensions of a partial order. A jump occurs in a linear extension if two consecutive elements are unrelated in the partial order. The jump number problem is to find a linear extension of the ordered set which contains the smallest possible number of jumps. We discuss a decomposition approach for this problem from an algorithmic point of view. Based on this some new classes of partial orders are identified, for which the problem is polynomially solvable.     

Performance comparison of several priority schemes with priority jumps

In this paper, we consider several discrete-time priority queues with priority jumps. In a priority scheduling scheme with priority jumps, real-time and non-real-time packets arrive in separate queues, i.e., the high- and low-priority queue respectively. In order to deal with possibly excessive delays however, non-real-time packets in the low-priority queue can in the course of time jump to the high-priority queue. These packets are then treated in the high-priority queue as if they were real-time packets. Many criteria can be used to decide when packets of the low-priority queue jump to the high-priority queue. Some criteria have already been introduced in the literature, and we first overview this literature. Secondly, we propose and analyse a new priority scheme with priority jumps. Finally, we extensively compare all cited schemes. The schemes all differ in their jumping mechanism, based on a certain jumping criterion, and thus all have a different performance. We show the pros and cons of each jumping scheme.