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风险建模是确定有多少风险存在于一个特定的企业、投资或一系列的现金流中。
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我们提供的风险建模Financial risk modeling及其相关学科的代写,服务范围广, 其中包括但不限于:
- Statistical Inference 统计推断
- Statistical Computing 统计计算
- Advanced Probability Theory 高等楖率论
- Advanced Mathematical Statistics 高等数理统计学
- (Generalized) Linear Models 广义线性模型
- Statistical Machine Learning 统计机器学习
- Longitudinal Data Analysis 纵向数据分析
- Foundations of Data Science 数据科学基础
统计代写|风险建模代写Financial risk modeling代考|The Case of Fleeting Orders
Estimates vary by the trading platform, sample period and sample stocks, but the range of limit order “cancellations” documented in the literature is generally between one-tenth and two-thirds of all order submissions for US-based equities. 1 While this is a significant proportion of total orders submitted, the focus of both theoretical and empirical finance has been on limit order “executions.” In studies that do model limit order cancellations, all cancellations are usually treated as homogenous or are characterized by a homogeneous index, which is the same for all limit orders. Such characterization often leads to misspecified distributions relative to the empirical properties exhibited by order cancellations.
Empirical observation of limit order termination shows that most of the nonmarketable limit orders submitted to the order book end up being cancelled without execution and the majority of cancelled orders get cancelled within a very short time. Figure $2.1$ presents the Weibull probability plot for the survival to cancellation probability $S(t)$ as a function of limit order duration $t$ for ask limit orders for one stock, Comcast Corporation (ticker: CMCSA), submitted via the INET ECN during regular trading hours on September 20,2006 . The limit order durations are marked on the logarithmic scale on the horizontal axis, while the monotonic double-negative logarithmic transformations $\sim \ln (\sim \ln (S(t)))$ of the order survival-to-cancellation function are reported on the vertical axis. The six equidistant dashed vertical lines on the graph mark the duration times $(0.01,0.1,1,10,100$ and 1000 seconds) since the limit order submission. ${ }^{2}$ Between 50 and 90 percent of limit orders in each order
aggressiveness strata (where aggressiveness is measured by the tick distance from the best same-side quote) are cancelled within two seconds after the order submission.
The four equidistant dashed horizontal lines are drawn at the levels corresponding to the survival rates 99 percent, 90 percent, 35 percent and $0.0001$ percent. Those values are chosen so that the incremental distances between the horizontal lines on the doublenegative logarithmic scale $\ln (\ln (0.90) / \ln (0.99)) \approx \ln (\ln (0.35) / \ln (0.90))$ $\approx \ln (\ln (0.0001) / \ln (0.35)) \approx \ln (10)$ are approximately equal to the incremental distances $\ln (10)$ between the consecutive vertical lines on the log-duration scale. Note that if order cancellations in any order aggressiveness category occurred according to the Weibull distribution, which is a popular choice of the survival function literature, then the survivalto-cancellation function $S(t)=\exp (A t \beta)$ in the transformed scales would be plotted as a straight line with slope $\sim \beta$. While the constancy of the Weibull parameter $0<\beta<1$ can be accepted if our focus is exclusively on relatively large times to cancellation, approaching the fleeting orders with the constant Weibull parameter assumption is clearly inappropriate.
While this is an illustration for one stock-day, our empirical analysis finds that this pattern is robust. Yet, apart from a recent paper by Hasbrouck and Saar (2007), these fleeting orders have not been the focus of any study. There must be reasons why traders or algorithms submit limit orders and subsequently cancel their orders within such a short period of time.
统计代写|风险建模代写Financial risk modeling代考|Literature review
A trader submitting an order to a limit order platform can choose between placing a marketable limit order (which gets immediate execution at the best prevailing price) or a limit order that enters the book and awaits execution. Once the order is in the book, it “risks” termination either by execution or by cancellation. Liu (2009) analyses the relation between limit order submission risk and monitoring costs borne by the trader. Limit order traders face two types of risk – first, they may be picked off due to expected price changes and second, they face the possibility of nonexecution. To mitigate these risks traders monitor the market and cancel or revise their orders as needed. But monitoring is costly, resulting in a trade-off between the cost of monitoring and the risks of limit order submission. The theoretical model predicts that if the stock is actively traded, limit order submission risks and order cancellations/revisions are positively related. Stocks with wide bid-ask spreads have lower rates of order cancellations and large capitalization stocks have lower costs of gathering information (and hence more intense monitoring of limit orders) and therefore more order revisions and cancellations. However, the empirical evidence from our study suggests that this is not the case. Apart from stock characteristics, order characteristics are also related to the rates of cancellation. Menkhoff and Schmeling (2005) separate limit orders into those that are aggressively priced – “screen orders ${ }^{\prime \prime}$ – and ordinary ones that wait in the book. They find that screen orders have a much lower cancellation rate than ordinary limit orders. In a study that focuses on time to cancellation of limit orders, Eisler et al. (2007) show that to correctly model the empirical properties of a limit order book and price formation therein, it is essential to specify a correct functional form for the cancellation process. They find that the transaction time,
the first passage time, the time to (first) fill and time to cancel are best described as asymptotically power-law distributed. In contrast, Challet and Stinchcombe (2003) show that for four highly liquid stocks on the Island ECN’s order book, ${ }^{4}$ the distribution for cancelled orders seems to have an algebraic decay with particular numerical values of the exponent. ${ }^{5}$ Rosu (2009) proposes a continuous time model of price formation and shows that to generate results that are close to those observed in the actual data, incorporating order cancellations is important.
While all the above studies tangentially focus on order cancellation, to our knowledge the first paper to actually make the distinction between order cancellations at longer durations and “fleeting order” cancellations is Hasbrouck and Saar (2002). In that version of their paper they use order data from the Island ECN and find that close to 28 percent of all visible submitted orders are cancelled within two seconds. They coin the term “fleeting orders” to describe these very short-lived orders. Although it is the first to describe fleeting orders, the 2002 study does not focus on these orders (in fact, these are eliminated from the sample in their subsequent analysis).
统计代写|风险建模代写Financial risk modeling代考|Data sample characteristics
Our sample comprises of the Nasdaq 100 stocks and the sample period is July-December 2006. We use the first three months (63 trading days) for estimation purposes and the next three for out-of-sample robustness checks. Our data comes from several sources. We use limit order placement and cancellation data from the INET ECN. The ITCH@ data feed from INET provides anonymous histories for all limit orders – when the orders were placed, modified, cancelled and executed – for all stocks that are traded on that platform. We use CRSP data for our firm-specific covariates and TAQ data from the NYSE to build the “National Best Bid and Offer” (NBBO) series of spreads and depths for our sample stocks. Additionally, we use earnings announcements data from I/B/E/S to partition our sample days into anticipated news days versus nonnews days in order to check the robustness of our estimates.
风险建模代写
统计代写|风险建模代写Financial risk modeling代考|The Case of Fleeting Orders
估计值因交易平台、样本期和样本股票而异,但文献中记载的限价订单“取消”范围通常在美国股票所有订单提交的十分之一到三分之二之间。1 虽然这在提交的订单总数中占很大比例,但理论和实证金融的重点一直是限价订单“执行”。在对限价单取消建模的研究中,所有取消通常被视为同质的,或者以同质指数为特征,这对于所有限价单都是相同的。这种表征通常会导致与订单取消所表现出的经验特性相关的错误指定分布。
限价单终止的经验观察表明,提交到订单簿的大部分非流通限价单最终都被取消而没有执行,并且大部分被取消的订单在很短的时间内被取消。数字2.1显示了生存到取消概率的 Weibull 概率图小号(吨)作为限价单持续时间的函数吨2006 年 9 月 20 日在正常交易时间内通过 INET ECN 提交的对一只股票 Comcast Corporation(股票代码:CMCSA)的询价限价单。限价单持续时间标记在横轴的对数刻度上,而单调双负对数变换∼ln(∼ln(小号(吨)))在垂直轴上报告了订单生存到取消函数。图表上的六条等距垂直虚线标记持续时间(0.01,0.1,1,10,100和 1000 秒)自限价单提交后。2每个订单中有 50% 到 90% 的限价订单
进取性分层(进取性通过与最佳同侧报价的刻度距离来衡量)在订单提交后两秒内被取消。
四个等距的水平虚线绘制在对应于存活率 99%、90%、35% 和0.0001百分。选择这些值是为了使双负对数刻度上水平线之间的增量距离ln(ln(0.90)/ln(0.99))≈ln(ln(0.35)/ln(0.90)) ≈ln(ln(0.0001)/ln(0.35))≈ln(10)大约等于增量距离ln(10)在对数持续时间刻度上的连续垂直线之间。请注意,如果任何订单攻击性类别中的订单取消是根据 Weibull 分布发生的,这是生存函数文献的流行选择,那么生存到取消函数小号(吨)=经验(一种吨b)在转换后的比例尺中将被绘制为一条带斜率的直线∼b. 而 Weibull 参数的恒定性0<b<1如果我们只关注相对较大的取消时间,则可以接受,使用恒定的 Weibull 参数假设来处理转瞬即逝的订单显然是不合适的。
虽然这是一个股票日的说明,但我们的实证分析发现这种模式是稳健的。然而,除了 Hasbrouck 和 Saar(2007 年)最近发表的一篇论文之外,这些转瞬即逝的秩序并未成为任何研究的重点。交易者或算法在如此短的时间内提交限价单并随后取消其订单肯定是有原因的。
统计代写|风险建模代写Financial risk modeling代考|Literature review
向限价订单平台提交订单的交易者可以选择下达可交易限价订单(以最佳现行价格立即执行)或进入账簿并等待执行的限价订单。一旦订单在账簿上,它就会“冒”被执行或取消而终止的风险。Liu(2009)分析了限价单提交风险与交易者承担的监控成本之间的关系。限价单交易者面临两种风险——第一,他们可能因预期的价格变化而被淘汰,第二,他们面临不执行的可能性。为了减轻这些风险,交易者监控市场并根据需要取消或修改他们的订单。但监控成本高昂,需要在监控成本和提交限价单的风险之间进行权衡。理论模型预测,如果股票交易活跃,限价单提交风险和订单取消/修改呈正相关。买卖价差较大的股票取消订单的比率较低,而大市值股票收集信息的成本较低(因此对限价订单的监控更加严格),因此订单修改和取消的次数也更多。然而,我们研究的经验证据表明情况并非如此。除了库存特征外,订单特征还与取消率有关。Menkhoff 和 Schmeling (2005) 将限价订单分为激进定价的订单——“屏幕订单” 买卖价差较大的股票取消订单的比率较低,而大市值股票收集信息的成本较低(因此对限价订单的监控更加严格),因此订单修改和取消的次数也更多。然而,我们研究的经验证据表明情况并非如此。除了库存特征外,订单特征还与取消率有关。Menkhoff 和 Schmeling (2005) 将限价订单分为激进定价的订单——“屏幕订单” 买卖价差较大的股票取消订单的比率较低,而大市值股票收集信息的成本较低(因此对限价订单的监控更加严格),因此订单修改和取消的次数也更多。然而,我们研究的经验证据表明情况并非如此。除了库存特征外,订单特征还与取消率有关。Menkhoff 和 Schmeling (2005) 将限价订单分为激进定价的订单——“屏幕订单” 除了库存特征外,订单特征还与取消率有关。Menkhoff 和 Schmeling (2005) 将限价订单分为激进定价的订单——“屏幕订单” 除了库存特征外,订单特征还与取消率有关。Menkhoff 和 Schmeling (2005) 将限价订单分为激进定价的订单——“屏幕订单”′′——还有那些在书中等待的普通人。他们发现屏幕订单的取消率远低于普通限价订单。在一项关注取消限价单的时间的研究中,Eisler 等人。(2007) 表明,要正确模拟限价订单簿的经验属性和其中的价格形成,必须为取消过程指定正确的函数形式。他们发现交易时间,
第一次通过时间、(第一次)填充时间和取消时间最好描述为渐近幂律分布。相比之下,Challet 和 Stinchcombe (2003) 表明,对于 Island ECN 订单簿上的四只高流动性股票,4取消订单的分布似乎具有代数衰减,具有特定的指数数值。5Rosu (2009) 提出了价格形成的连续时间模型,并表明要产生接近实际数据中观察到的结果,结合订单取消很重要。
虽然上述所有研究都只关注订单取消,但据我们所知,第一篇真正区分较长时间的订单取消和“短暂订单”取消的论文是 Hasbrouck 和 Saar (2002)。在该版本的论文中,他们使用 Island ECN 的订单数据,发现近 28% 的可见提交订单在两秒内被取消。他们创造了“转瞬即逝的订单”一词来描述这些非常短暂的订单。虽然它是第一个描述转瞬即逝的订单,但 2002 年的研究并未关注这些订单(事实上,这些订单在随后的分析中已从样本中剔除)。
统计代写|风险建模代写Financial risk modeling代考|Data sample characteristics
我们的样本包括纳斯达克 100 股,样本期为 2006 年 7 月至 2006 年 12 月。我们将前三个月(63 个交易日)用于估计目的,后三个月用于样本外稳健性检查。我们的数据来自多个来源。我们使用来自 INET ECN 的限价订单放置和取消数据。来自 INET 的 ITCH@ 数据馈送为在该平台上交易的所有股票提供所有限价订单的匿名历史记录——订单的下达、修改、取消和执行时间。我们将 CRSP 数据用于我们公司特定的协变量和来自纽约证券交易所的 TAQ 数据,为我们的样本股票构建“全国最佳买入价和卖出价”(NBBO)系列的价差和深度。此外,
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金融工程代写
金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题,以及设计新的和创新的金融产品。
非参数统计代写
非参数统计指的是一种统计方法,其中不假设数据来自于由少数参数决定的规定模型;这种模型的例子包括正态分布模型和线性回归模型。
广义线性模型代考
广义线性模型(GLM)归属统计学领域,是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。
术语 广义线性模型(GLM)通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归,以及方差分析和方差分析(仅含固定效应)。
有限元方法代写
有限元方法(FEM)是一种流行的方法,用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。
有限元是一种通用的数值方法,用于解决两个或三个空间变量的偏微分方程(即一些边界值问题)。为了解决一个问题,有限元将一个大系统细分为更小、更简单的部分,称为有限元。这是通过在空间维度上的特定空间离散化来实现的,它是通过构建对象的网格来实现的:用于求解的数值域,它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统,以模拟整个问题。然后,有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。
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随机分析代写
随机微积分是数学的一个分支,对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。
时间序列分析代写
随机过程,是依赖于参数的一组随机变量的全体,参数通常是时间。 随机变量是随机现象的数量表现,其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值(如1秒,5分钟,12小时,7天,1年),因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中,往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录,以得到其自身发展的规律。
回归分析代写
多元回归分析渐进(Multiple Regression Analysis Asymptotics)属于计量经济学领域,主要是一种数学上的统计分析方法,可以分析复杂情况下各影响因素的数学关系,在自然科学、社会和经济学等多个领域内应用广泛。
MATLAB代写
MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中,其中问题和解决方案以熟悉的数学符号表示。典型用途包括:数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发,包括图形用户界面构建MATLAB 是一个交互式系统,其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题,尤其是那些具有矩阵和向量公式的问题,而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问,这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展,得到了许多用户的投入。在大学环境中,它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域,MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要,工具箱允许您学习和应用专业技术。工具箱是 MATLAB 函数(M 文件)的综合集合,可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。