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# 金融代写|金融工程代写FINANCIAL ENGINEERING代写|ICEFE2022 Definitions

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## 金融代写|金融工程代写FINANCIAL ENGINEERING代写|Definitions

A European call option is a contract giving the holder the right to buy an asset, called the underlying, for a price $X$ fixed in advance, known as the exercise price or strike price, at a specified future time $T$, called the exercise or expiry time. A European put option gives the right to sell the underlying asset for the strike price $X$ at the exercise time $T$.

An American call or put option gives the right to buy or, respectively, to sell the underlying asset for the strike price $X$ at any time between now and a specified future time $T$, called the expiry time. In other words, an American option can be exercised at any time up to and including expiry.

The term ‘underlying asset’ has quite general scope. Apart from typical assets such as stocks, commodities or foreign currency, there are options on stock indices, interest rates, or even on the snow level at a ski resort. Some underlying assets may be impossible to buy or sell. The option is then cleared in cash in a fashion which resembles settling a bet. For example, the holder of a European call option on the Standard and Poor Index (see page 141) with strike price 800 will gain if the index turns out to be 815 on the exercise date. The writer of the option will have to pay the holder an amount equal to the difference $815-800=15$ multiplied by a fixed sum of money, say by $\$ 100$. No payment will be due if the index turns out to be lower than 800 on the exercise date. An option is determined by its payoff, which for a European call is $$\begin{cases}S(T)-X & \text { if } S(T)>X, \ 0 & \text { otherwise. }\end{cases}$$ This payoff is a random variable, contingent on the price$S(T)$of the underlying on the exercise date$T$. (This explains why options are often referred to as contingent claims.) It is convenient to use the notation $$x^{+}= \begin{cases}x & \text { if } x>0 \ 0 & \text { otherwise. }\end{cases}$$ ## 金融代写|金融工程代写FINANCIAL ENGINEERING代写|Put-Call Parity In this section we shall make an important link between the prices of European call and put options. Consider a portfolio constructed by and writing and selling one put and buying one call option, both with the same strike price$X$and exercise date$T$. Adding the payoffs of the long position in calls and the short position in puts, we obtain the payoff of a long forward contract with forward price$X$and delivery time$T$. Indeed, if$S(T) \geq X$, then the call will pay$S(T)-X$and the put will be worthless. If$S(T)<X$, then the call will be worth nothing and the writer of the put will need to pay$X-S(T)$. In either case, the value of the portfolio will be$S(T)-X$at expiry, the same as for the long forward position, see Figure 7.2. As a result, the current value of such a portfolio of options should be that of the forward contract, which is$S(0)-X \mathrm{e}^{-r T}$, see Remark 6.3. This motivates the theorem below. Even though the theorem follows from the above intuitive argument, we shall give a different proof with a view to possible generalisations. ## 金融工程代写 ## 金融代写|金融工程代写FINANCIAL ENGINEERING代写|Definitions 欧式看涨期权是一种合约，渽予持有人以一定价格购买称为标的资产的权利$X$在特定的末来时间预先固定，称为行使价或行使价$T$，称为行使或到期时间。欧式看跌期权赋予以行使价出售标的资产的权利$X$在运动时间$T$. 美式看张或看跌期权分别赋予以行使价购买或出售标的资产的权利$X$从现在到指定的末来时间之间的任何时间$T$，称为到期时间。 换句话脱，美式期权可以在到期前（包括到期）的任何时间行使。 “标的资产”一词具有相当簉统的范围。除了股票、大宗商品或外汇等典型诏产外，还有股票指数、利率甚至㳑雪胜地雪位的期权。 一些标的资产可能无法买卖。然后以类似于结算赌注的方式以现金清算该选项。例如，如果该指数在行权日的结果为 815 ，则执行 价格为 800 的标准普尔指数 (见第 141 页) 的欧洲看涨期权的持有者将获得收益。期权的卖方必须向持有人支付相当于差楁的金 额$815-800=15$乘以固定金额，例如$\$100$. 如果指数在行使日低于 800 ，则无需支付任何款项。

$${S(T)-X \quad \text { if } S(T)>X, 0 \quad \text { otherwise. }$$

$$x^{+}= \begin{cases}x & \text { if } x>00 \quad \text { otherwise. }\end{cases}$$

## 金融代写|金融工程代写FINANCIAL ENGINEERING代写|Put-Call Parity

$T$. 确实，如果 $S(T) \geq X$ ，然后通话将支付 $S(T)-X$ 并且看跌期权将一文不值。如果 $S(T)<X$ ，那么看涨期权将一文不

## 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。