Error analysis of finite difference and Markov chain approximations for option pricing

Mijatovi? and Pistorius proposed an efficient Markov chain approximation method for pricing European and barrier options in general one‐dimensional Markovian models. However, sharp convergence rates of this method for realistic financial payoffs, which are nonsmooth, are rarely available. In this paper, we solve this problem for general one‐dimensional diffusion models, which play a fundamental role in financial applications. For such models, the Markov chain approximation method is equivalent to the method of lines using the central difference. Our analysis is based on the spectral representation of the exact solution and the approximate solution. By establishing the convergence rate for the eigenvalues and the eigenfunctions, we obtain sharp convergence rates for the transition density and the price of options with nonsmooth payoffs. In particular, we show that for call‐/put‐type payoffs, convergence is second order, while for digital‐type payoffs, convergence is generally only first order. Furthermore, we provide theoretical justification for two well‐known smoothing techniques that can restore second‐order convergence for digital‐type payoffs and explain oscillations observed in the convergence for options with nonsmooth payoffs. As an extension, we also establish sharp convergence rates for European options for a rich class of Markovian jump models constructed from diffusions via subordination. The theoretical estimates are confirmed using numerical examples.     

The (potential) demise of HRM?

This article seeks to provoke that human resource management (HRM), both as an academic field of study and as a form of professional practice, is at risk of impoverishment. The main reasoning for this is because of ideological individualism and marketisation with an attendant neglect on wider organisational, employee, and societal concerns. Following a review of the context of financialised capitalism, three contemporary developments in HRM are used to illustrate the argument: reward strategies, talent management, and high performance work systems. Implications for the practice of HRM and the way the subject area is taught in mainstream business schools are considered.     

No‐arbitrage implies power‐law market impact and rough volatility

Market impact is the link between the volume of a (large) order and the price move during and after the execution of this order. We show that in a quite general framework, under no‐arbitrage assumption, the market impact function can only be of power‐law type. Furthermore, we prove this implies that the macroscopic price is diffusive with rough volatility, with a one‐to‐one correspondence between the exponent of the impact function and the Hurst parameter of the volatility. Hence, we simply explain the universal rough behavior of the volatility as a consequence of the no‐arbitrage property. From a mathematical viewpoint, our study relies, in particular, on new results about hyper‐rough stochastic Volterra equations.     

网络经济下的企业竞合关系的演变

随着信息技术的快速发展，社会经济转型加速，网络经济已经形成并迅速发展。企业的经济运行环境随之发生了巨大的变化，传统的企业间竞合关系认识以及相关战略已经很难适应网络经济下企业的发展需要。本文在回顾西方经济理论关于合作的理论的基础上，从网络经济的诸多特征出发，依据交易成本理论和博弈论方法分析了网络经济下企业广泛开展合作的动因，并介绍了企业合作的实现形式。     

电感耦合等离子体发射光谱法测定蜂蜜中7种矿物元素的含量

为了快速直接测定蜂蜜中多种矿物元素的含量,采用电感耦合等离子体发射光谱(ICP-AES)法建立了同时测定蜂蜜中钙、钾、镁、钠、锌、铁、铜7种矿物元素含量的方法,考察了方法的标准曲线线性关系、检出限、精密度和准确度,讨论了前处理方法、不同产地以及蜜源植物种类对各元素含量的影响。结果表明:线性相关系数达到0.999 9以上,方法检出限为0.003～0.030 mg/L,相对标准偏差低于2%,回收率为88.66%～105.31%;不同产地的洋槐蜜中,河北洋槐蜜的钙、钾含量明显高于其他地区,广西洋槐蜜的钠、铁含量最高;不同蜜源植物的蜂蜜中,河北枣花蜜的铁含量最高,野生蜜中各种矿物元素都较为丰富。电感耦合等离子体发射光谱法可以快速、同时测定蜂蜜中多种矿物元素含量,方法简便易行,结果准确可靠,可为蜂蜜品质鉴定以及人们对蜂蜜的合理选择提供参考。     

一种基于自适应相似矩阵的谱聚类算法

为了消除在构建谱聚类算法的相似矩阵时,高斯核函数中尺度参数的波动影响,构建了一种自适应相似矩阵,并应用到谱聚类算法中。自适应相似矩阵中数据点间的距离度量采用测地距离算法,相距较近的两点间的距离近似于欧氏距离,相距较远的两点则先根据欧氏距离得到每个数据点的k个近邻点,然后累加近邻点的测地距离,由此得到每对数据点间的最短距离。两点间的局部密度用共享近邻的定义来表示,更好地刻画了数据集的本征结构。在5个人工数据集和国际通用UCI数据库中的5个真实数据集上进行实验。实验结果表明,所提算法的聚类准确率高于对比算法的准确率,对复杂分布数据有很强的自适应能力。研究成果为数据挖掘及机器学习提供了思路和方法。     

动液面谱减法滤波

动液面滤波是油井检测动液面的关键技术之一。文章利用谱减法处理油井动液面信号,消除背景噪声的影响,并改进谱减法应用到动液面滤波,取得较好的滤波效果,从而提高对液面反射波位置的辨识能力。     

PRICING DERIVATIVES ON MULTISCALE DIFFUSIONS: AN EIGENFUNCTION EXPANSION APPROACH

Using tools from spectral analysis, singular and regular perturbation theory, we develop a systematic method for analytically computing the approximate price of a large class of derivative‐assets. The payoff of the derivative‐assets may be path‐dependent. In addition, the process underlying the derivatives may exhibit killing (i.e., jump to default) as well as combined local/nonlocal stochastic volatility. The nonlocal component of volatility may be multiscale, in the sense that it may be driven by one fast‐varying and one slow‐varying factor. The flexibility of our modeling framework is contrasted by the simplicity of our method. We reduce the derivative pricing problem to that of solving a single eigenvalue equation. Once the eigenvalue equation is solved, the approximate price of a derivative can be calculated formulaically. To illustrate our method, we calculate the approximate price of three derivative‐assets: a vanilla option on a defaultable stock, a path‐dependent option on a nondefaultable stock, and a bond in a short‐rate model.     

基于高光谱曲线的马铃薯与其他主要作物光谱差异性分析

[目的]文章以马铃薯关键生长期——结薯期为测量时点,以马铃薯和玉米、大豆、水稻为研究对象,开展高光谱曲线特征差异性研究。[方法]为更好地描述马铃薯与其他作物的光谱差异,创建高光谱反射率差异性指数、高光谱一阶导数差异性指数、高光谱红边幅值差异性指数、高光谱曲率差异性指数及高光谱植被指数差异性指数。[结果](1)马铃薯与玉米、大豆、水稻3种作物光谱曲线具有明显差异,马铃薯与玉米的反射率值在480nm附近蓝色波段位置差异最显著,差异性指数值为67.866%,与大豆、水稻的最大差异性指数值分别为49.068%、57.559%,均位于550nm附近绿色波峰位置;(2)作物光谱曲线经一阶导数变换运算,马铃薯与其他作物间的光谱差异被显著放大,在近红外波段放大程度最显著;(3)马铃薯与玉米、大豆、水稻高光谱曲率差异性指数最大值均位于波长750nm附近,差异性指数值分别为78.365%、63.471%、80.882%;(4)常用植被指数中,比值植被指数、增强型植被指数可显著区分马铃薯与玉米、大豆、水稻。[结论]差异性分析结果为农作物空间分布遥感识别提供了技术支撑。     

有机波谱分析课程教学改革的探索与实践

简要介绍了有机波谱分析课程的教学内容、目的、任务及应用,重点介绍了:①有机波谱分析课程教学内容的改革;②有机波谱分析课程教学方法的改进;③识谱解谱是学生学习的核心;④有机波谱分析课程教学模式的改革。