Posted on Categories:Financial Mathematics, 金融代写, 金融数学

# 数学代写|金融数学代写Financial Mathematics代考|MT4551 Analysis of Time Aggregated Data

avatest™

avatest.org™金融数学Financial Mathematics代写，免费提交作业要求， 满意后付款，成绩80\%以下全额退款，安全省心无顾虑。专业硕 博写手团队，所有订单可靠准时，保证 100% 原创。avatest.org™， 最高质量的金融数学Financial Mathematics作业代写，服务覆盖北美、欧洲、澳洲等 国家。 在代写价格方面，考虑到同学们的经济条件，在保障代写质量的前提下，我们为客户提供最合理的价格。 由于统计Statistics作业种类很多，同时其中的大部分作业在字数上都没有具体要求，因此金融数学Financial Mathematics作业代写的价格不固定。通常在经济学专家查看完作业要求之后会给出报价。作业难度和截止日期对价格也有很大的影响。

avatest™ 为您的留学生涯保驾护航 在网课代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的网课代写服务。我们的专家在金融数学Financial Mathematics代写方面经验极为丰富，各种金融数学Financial Mathematics相关的作业也就用不着 说。

## 数学代写|金融数学代写Financial Mathematics代考|Realized Volatility and Econometric Models

Estimating volatility using high frequency data has received a great deal of attention as intra-day strategies became more prevalent. In the low frequency (daily) level some estimators based on select prices were presented in Chapter 2. Intra-day dynamics of volatility is of interest to traders and is usually not fully captured by the stock price indicators sampled during the day. If higher frequency data are used to estimate volatility of lower frequency data, it is important to know the model for the return at the lower frequency. To illustrate this, we consider data observed at two time scales; although they are somewhat at low frequency level, the concept can be easily extended to the high frequency context. If $r_{t, i}$ is the $i$ th day return in $t$ th month, the $t$ th month return assuming there ‘ $n$ ‘ trading days, $r_{t}^{m}=\sum_{i=1}^{n} r_{t, i}$. Note that $\sigma_{m}^{2}=\operatorname{Var}\left(r_{t}^{m} \mid F_{t-1}\right)=\sum_{i=1}^{n} \operatorname{Var}\left(r_{t, i} \mid F_{t-1}\right)+2 \sum_{i<j} \operatorname{Cov}\left(r_{t, i}, r_{t, j} \mid F_{t-1}\right)$. If $r_{t, i}$ is a white noise sequence, then
$$\hat{\sigma}{m}^{2}=\frac{n}{n-1} \sum{i=1}^{n}\left(r_{t, i}-\bar{r}{t}\right)^{2} .$$ But we had observed that in the high frequency data, returns do exhibit some serial correlation and so adjusting (4.39) for serial correlation is important to get a more accurate estimate of volatility. A simpler estimate of $\sigma{m}^{2}$ is the so-called realized volatility $\left(\mathrm{RV}{t}\right)$ $$\mathrm{RV}{t}=\sum_{i=1}^{n} r_{t, i}^{2}$$

## 数学代写|金融数学代写Financial Mathematics代考|Volatility and Price Bar Data

The price as assumed earlier is to follow a random walk model. Therefore, price changes (thus returns) over a time interval are distributed with mean zero and variance that is proportional to the length of the interval. Assuming that the prices follow continuous sample paths although the trading is closed for a certain duration and when trading is open, the actual transactions occur at discrete points in time. Treating the trading day as represented in a unit interval $[0,1]$ with $[0, f]$ representing the ‘market close’ time and $[f, 1]$ as ‘open’ time, it is shown that an estimator of volatility
$$\hat{\sigma}{1}^{2}=\frac{\left(O{1}-C_{0}\right)^{2}}{2 f}+\frac{\left(C_{1}-O_{1}\right)^{2}}{2(1-f)},$$
has efficiency two compared to the usual estimator, $\hat{\sigma}{0}^{2}=\left(C{1}-C_{0}\right)^{2}$ based on the closing prices of two successive trading days. This suggests clearly the inclusion of additional data points, such as opening price, which can be quite informative. Garman and Klass (1980) [158] suggest these and other estimators which are superior to the classical estimator of volatility $\hat{\sigma}_{0}^{2}$. It is argued that the high and low prices contain information regarding the volatility during the trading period and a composite estimator that is proposed,
$$\hat{\sigma}{2}^{2}=a \frac{\left(O{1}-C_{0}\right)^{2}}{f}+(1-a) \frac{\left(H_{1}-L_{1}\right)^{2}}{(1-f) \ln 2}$$
with optimal choice of ‘ $a$ ‘ $=0.17$ yields even higher efficiency.

## 数学代写|金融数学代写Financial Mathematics代考|Realized Volatility and Econometric Models

$$\hat{\sigma} m^{2}=\frac{n}{n-1} \sum i=1^{n}\left(r_{t, i}-\bar{r} t\right)^{2} .$$

$$\mathrm{RV} t=\sum_{i=1}^{n} r_{t, i}^{2}$$

## 数学代写|金融数学代写Financial Mathematics代考|Volatility and Price Bar Data

$$\hat{\sigma} 1^{2}=\frac{\left(O 1-C_{0}\right)^{2}}{2 f}+\frac{\left(C_{1}-O_{1}\right)^{2}}{2(1-f)},$$

## 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。