### 统计代写|风险建模代写Financial risk modeling代考|Principal components of execution and cancellation probabilities

statistics-lab™ 为您的留学生涯保驾护航 在代写风险建模Financial risk modeling方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写风险建模Financial risk modeling代写方面经验极为丰富，各种代写风险建模Financial risk modeling相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|Principal components of execution and cancellation probabilities

We use the following covariates for our principal components analysis:

• Price = the INET average transaction price per share,
• Sprd = the INET inside spread,
• Range $=$ the five-minute INET price range,
• Disvol = the INET share volume from executions against displayed limit orders,
• Hinvol = the INET volume of executions against hidden orders inside the INET spread,
• Houtvol = the five-minute INET volume from executions against hidden orders on the edges of the INET bid-ask spread,
• Dep1 = the average displayed depth of the INET book at the best bid and ask prices,
• Dep5 = the average displayed depth of the INET order book at the top five ticks on bid and ask sides of the book, and
• Shrs = the number of outstanding common shares for each stock on June $30,2006 .$

Panel A of Table $2.5$ shows the correlation matrix for the above covariates. The majority of these variables have a coefficient of correlation of greater than 50 percent with at least one of the other variables. Given this, we apply principal component analysis to effect a dimension reduction. We extract the first five principal components for the stock-specific averages of our covariates Logprice $=\ln ($ Price $)$, Logsprd $=$ $\ln ($ Sprd-1), Logrange $=\ln ($ Range $), \quad$ Logdisvol $=\ln ($ Disvol $), \quad$ Loghinvol $=$ $\ln ($ Hinvol $), \quad$ Loghoutvol $=\ln ($ Houtvol $), \quad$ Logdep $1=\ln ($ Dep 1$), \quad$ Logdep5 $=$ $\ln ($ Dep5 $)$ and Logshrs $=\ln ($ Shrs $)$. The five principal components $P C 1, \ldots$, $P C S$ are constructed as linear combinations of the above covariates so that they have orthonormal loading coefficients and $P C 1$ is chosen to explain the largest proportion of variation in the covariates, $P C 2$ explains the largest proportion of the variation that is left unexplained by the first component, $P C 3$ explains the largest proportion of variance unexplained by the first two components and so forth. The linear combination coefficients for each principal component are reported in Panel C of Table $2.5$. The first five factors $P C 1, \ldots, P C 5$ are related to our covariates by the

## 统计代写|风险建模代写Financial risk modeling代考|The mixture of distributions model

We began our analysis by illustrating order cancellation rates for one stock, Comcast (CMCSA) – showing the high rates of cancellation at very short durations, which then taper off as time increases. We then showed that this pattern is robust across stocks. The dynamics of order cancellation at very short durations differ from those at longer time intervals. We use these observations to posit that instead of specifying one distribution to model order cancellations, a better approach would be to formulate a mixture of distributions – one that draws the fleeting orders from one distribution and longer duration orders from another.

## 统计代写|风险建模代写Financial risk modeling代考|Assumptions and notation

Assume we have access to the complete history of a limit order $k$, which was entered into the limit order book at time $T_{0}$. Prior to the limit order entering the book, the observed covariates capturing the market conditions were at the level $x_{k 0}$. Assume that the first change of the covariates to the new level $x_{k 1}$ occurs at time $T_{1}$, within $t_{k 1}$ seconds since the order arrival; the second change of the covariates to the new level $x_{k 2}$ occurs at time $T_{2}$, within $t_{k 2}$ seconds since this limit order arrival; and so on, until termination of the limit order at time $T_{i(k)}$, within $t_{k i(k)}$ seconds after the order arrival and the covariates prior to the limit order termination stayed at the level $\boldsymbol{x}_{k i(k)}$. Assume there are three possible causes for limit order termination: (1) cancellation, (2) full execution, and (3) censoring. In addition, we may allow for the possibility of partial executions during the lifetime of the limit order.

Upon arrival, the limit order assumes one of the two types: (1) fleeting or (2) regular (non-fleeting). The newly arrived order is fleeting with probability $\pi\left(x_{k 0}\right)=\exp \left(-\pi^{\prime} x_{k 0}\right) /\left(1+\exp \left(-\pi^{\prime} x_{k 0}\right)\right)$ and non-fleeting with the complementary probability $1 /\left(1+\exp \left(-\pi^{\prime} x_{k 0}\right)\right)$. If the order is fleeting then the risk of its cancellation depends on the level of covariates just prior to (or, alternatively, immediately after) this limit order arrival, with the hazard rate of the cancellation given by the index function $v\left(x_{k 0}\right)=\exp \left(v^{\prime} x_{k 0}\right)$ (or, alternatively, by $\left.v\left(x_{k 1}\right)=\exp \left(v^{\prime} x_{k 1}\right)\right)$. If the order is non-fleeting then the instantaneous risk of its cancellation depends on the contemporaneous level of covariates; therefore, for a non-fleeting limit order observed within the duration episode $\Delta t_{k i}$, the hazard rate of its cancellation is given by the index function $\xi\left(x_{k i}\right)=\exp \left(\xi^{\prime} x_{k i}\right)$. Conditional on the limit order being “at risk” of execution within the episode $\Delta t_{k i}$ both fleeting and non-fleeting orders are subject to execution risk, which is characterized by its hazard rate $\mu\left(\boldsymbol{x}{k i}\right)=\exp \left(\mu^{\prime} x{k i}\right)$. The indicator of being “at risk” of being executed within the duration episode $\Delta t_{k i}$ is given by $R_{k i}=R\left(x_{k i}\right)$, which is a zero-one switch function of covariates $\boldsymbol{x}{k i}$. In addition, the limit order history may also be censored at time $T{i(k)}$ without execution or cancellation, in which case it will be assumed that the censoring occurs independently of the execution and cancellation events.

## 统计代写|风险建模代写Financial risk modeling代考|Principal components of execution and cancellation probabilities

• 价格 = 每股 INET 平均交易价格，
• Sprd = INET 内部传播，
• 范围=五分钟的 INET 价格范围，
• Disvol = 根据显示的限价订单执行的 INET 份额数量，
• Hinvol = 针对 INET 价差内隐藏订单的 INET 执行量，
• Houtvol = 针对 INET 买卖价差边缘的隐藏订单执行的五分钟 INET 交易量，
• Dep1 = INET 图书在最佳买入价和卖出价下的平均显示深度，
• Dep5 = INET 订单簿在买盘和卖盘前五个分时的平均显示深度，以及
• Shrs = 6 月份每只股票的已发行普通股数量30,2006.

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。