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• 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

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|Cash Settlement as an Alternative to Actual Physical Settlement

Consider a forward contract requiring the delivery of a share of stock $T$ years from now (time 0 ) at the forward price $F$. The price of the stock at any time $t$ is denoted as $S_t$, so the price of the stock when delivery of the forward contract is scheduled to take place is $S_T$.
Let’s examine what happens if $S_T>F$ on the delivery date. In many such derivatives the parties to the contract can demand to take or make delivery. In this case, the short position in the contract delivers the stock to the long position in the contract in exchange for the payment $F$.

The payoff of the derivative is the net gain or loss for each party at the expiration of the derivative contract. Since the actual price of the stock at time $T$ is likely different from $F$, the economic result of the contract at time $T$ is that the long side gains (if $S_T-F$ is positive) or loses (if $S_T-F$ is negative). Specifically, the long position has a payoff of $S_T-F$ and the short position has a payoff of $F-S_T$. Note that the payoff of the long and short sides of the contract sum to 0 .
Forward payoff for a long position $=S_T-F$
Forward payoff for a short position $=F-S_T$
The two parties to the forward contract might be using the contract to control risk, not with the desire to ultimately exchange the stock. In that case the parties may do a cash settlement rather than a physical settlement. In a cash settlement the entire transaction is terminated or settled at time $T$ by exchanging the cash $S_T-F$. When $S_T>F$, the cash payment is from the short side of the contract to the long side, and vice versa.

Let’s return to the previous example of a forward contract between an airline company and a refinery regarding jet fuel. Rather than actually buying the jet fuel for the pre-specified price directly from the short side of the contract at the time of settlement, the two parties may agree that the long side of the contract (the airline company) may receive $S_T-F$ from the short side when $S_T-F>0$ and then buy the fuel in the spot market at the price $S_T$. Putting together the value $S_T-F$ from the forward contract and the expenditure of $S_T$ to purchase the jet fuel in the spot market generates a net expenditure of $F$ for the jet fuel, which is exactly what the airline company expected. If $F>S_T$ on the delivery date, we may view the long side as paying $F-S_T$ to the short side and buying the fuel in the spot market at the price $S_T$ which nets again to an expenditure of $F$ for the jet fuel, as the airline company expected. When $F=S_T$, the contract terminates with no value to either party. The analysis for the short side of the contract reveals that participation in the forward contract may be viewed as having the payoff $F-S_T$ which when combined with selling the jet fuel that they produced at $S_T$ nets sales proceeds of $F$ which is the price that was fixed through the forward contract.

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|Applications of Forward Contracts

Let’s look at a variety of examples to illustrate the diverse uses of forward contracts to manage risks.

Example 1.5: A U.S. importer of British beer establishes a long position in a three-month forward on 100,000 British pounds at $\$ 1.35$per pound. Assume today is August 26, 2022, and the spot exchange rate of the British pound price is$\$1.31$ per pound.

The importer establishes the long position to lock in the cost of importing the beer which is priced in the brewer’s local currency. The importer’s long position in the forward contract is fixing the costs of imports in three months in terms of U.S. dollars. Perhaps the short side of the contract is a speculator who has predicted that the exchange rate will fall substantially and will be settled with a positive value to the speculator.

## 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。

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