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## 金融代写|量化风险管理代写Quantitative Risk Management代考|JUMP-DIFFUSION MODEL

In the GARCH model, volatility changes gradually over time. In financial markets we do observe this sort of behavior, but we also see extreme events that seem to come out of nowhere. For example, on February 27, 2007, in the midst of otherwise calm markets, there were rumors that the Chinese central bank might raise interest rates. There was also some bad economic news in the United States. These two events contributed to what, by some measures, was a $-8$ standard deviation move in U.S. equity markets. A move of this many standard deviations would be extremely rare for most standard parametric distributions.
One popular way to generate this type of extreme return is to add a so-called jump term to our standard time-series model. This can be done by adding a second disturbance term, as follows
$$r_{t}=\alpha+\varepsilon_{t}+\left[I_{t}\right] u_{t}$$
Here, $r_{t}$ is the market return at time $t, \alpha$ is a constant drift term, and $\varepsilon_{t}$ is a mean zero diffusion term. As specified, our jump term has two components: $\left[I_{t}\right]$, an indicator variable that is either zero or one, and $u_{t}$, an additional disturbance term. Because it has a jump and a diffusion term, this time series model is referred to as a jump-diffusion model.

The jump-diffusion model is really just a mixture model. To get the type of behavior we want-moderate volatility punctuated by rare extreme events-we can set the standard deviation of $\varepsilon_{t}$ to relatively modest levels. We then specify the probability of $\left[I_{t}\right]$ equaling one at some relatively low level, and set the standard deviation of $u_{t}$ at a relatively high level. If we believe that extreme negative returns are more likely than extreme positive returns, we can also make the distribution of $u_{t}$ asymmetrical. $u_{t}$ does not have to have a mean of zero. GARCH and jump-diffusion are not mutually exclusive. By combining GARCH and jump-diffusion, we can model and understand a wide range of market environments and dynamics.

## 金融代写|量化风险管理代写Quantitative Risk Management代考|DOLLAR STANDARD DEVIATION

In risk management, when we talk about the standard deviation of a security, we are almost always talking about the standard deviation of the returns for that security. While this is almost always the case, there will be times when we want to express standard deviation and other risk parameters in terms of dollars (or euros, yen, etc.).

## 有限元方法代写

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## 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。