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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

## 金融代写|金融数学代写Financial Mathematics代考|Option Hedging Strategies

The previous section mostly discussed speculators in option contracts. Options can also be valuable opportunities for hedgers whose primary purpose is to reduce risk. The following examples illustrate the use of options for hedging purposes while illustrating the variety of options available to hedgers.

A producer of rings for college graduations may by concerned that the price of gold is going to rise prior to the spring when most graduation ceremonies are held. However, the jeweler needs to announce prices for the rings earlier in the year before the orders for rings are placed. If the manufacturer knew how many rings would be ordered in the months prior to graduation, the manufacturer could buy the gold now or could enter a forward contract to purchase the gold. But the manufacturer does not want to be heavily exposed to the risk that their forecasts may be quite erroneous and the firm would end up with a large surplus or shortage of gold. Options can come to the rescue. The firm might enter forward contracts for a low estimate of their gold usage and purchase a call option on the additional amount of gold to reach the high end of their estimates. The purchase price of the call option on gold may be reasonable when compared to the potential outlay involved with ordering too much or too little gold in the spot, forward, or futures markets.

Next, consider the uncertainty faced by farmers, food processors, and food exporters with regard to the prices of grains near an important harvest season. The farmer fears that the price of her crop will fall before it can be harvested and sold. But the farmer is concerned about entering a short position in a forward contract since if her crop fails she will still be responsible for settling the promise made to deliver the crop to satisfy the terms of the forward contract. A potentially attractive solution to the farmer’s dilemma is to purchase a put option on some or all of the anticipated harvest. The put option will lock in a minimum price while limiting the farmer’s downside risk to the purchase price of the option.

## 金融代写|金融数学代写Financial Mathematics代考|Put-Call Parity and Arbitrage

An important relationship exists between call option prices, $C$, and put option prices, $P$. The price of a European put option and European call option with the same underlying asset, same strike price $K$, and same expiration date $T$ must satisfy the following relationship known as put-call parity:
$$C+K e^{-r T}=P+S_{0}$$
From left to right, Equation $1.14$ can be expressed as “owning a call plus a bond is equivalent to owning a put plus the stock.” This well-known equation is often arranged differently or expressed with different notation. This particular arrangement is convenient for demonstrating why the relationship must be true in a well-functioning market with no arbitrage. The left and right sides of Equation $1.14$ can be viewed as payoff to two portfolios, A and B.

Portfolio A (left side): Buy a call on a stock + buy a zero-coupon bond that pays $K$ at time $T$.
Portfolio B (right side): Buy a put on the same stock + buy the stock.
Note that the two payoff columns on the right side of Table $1.2$ demonstrate that the total payoff to Portfolio $\mathrm{A}\left(S_{T}\right.$ or $\left.K\right)$ equals the total payoff to Portfolio B ( $S_{T}$ or $K$ ) whether the call option is exercised at expiration (i.e., $\left.S_{T}>K\right)$, or whether the put option is exercised $\left(K>S_{T}\right)$. Obviously, when $S_{T}=$ $K$ neither option has a value at expiration and portfolios A and B have equal values $(K)$. Since under all scenarios both portfolios have the same total payoffs, they must therefore be worth the same today. This means that Equation $1.14$ holds:
$$C+K e^{-r T}=P+S_{0} .$$

## 金融代写|金融数学代写Financial Mathematics代考|Put-Call Parity and Arbitrage

$$C+K e^{-r T}=P+S_{0}$$

$$C+K e^{-r T}=P+S_{0} .$$

## 有限元方法代写

assignmentutor™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。

assignmentutor™您的专属作业导师
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