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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|期权理论代写Mathematical Introduction to Options代考|COMBINATIONS OF OPTIONS

This is a book on option theory and many “how to” books are available giving very full descriptions of trading strategies using combinations of options. There is no point repeating all that stuff here. However, even the most theoretical reader needs a knowledge of how the more common combinations work, and why they are used; also, some useful intuitive pointers to the nature of time values are examined, before being more rigorously developed in later chapters. Most of the comments will be confined to combinations of European options.
(i) Call Spread (bull spread, capped call): This is the simplest modification of the call option. The payoff is similar to that of a call option except that it only increases to a certain level and then stops. It is used because option writers are often unwilling to accept the unlimited liability incurred in writing straight calls. The payoff diagram is shown in the first graph of Figure 2.6.
It is important to understand that a European call spread (and indeed any of the combinations described below) can be created by combining simple options. The second graph of Figure $2.6$ shows how a call spread is merely a combination of a long call (strike $X_1$ ) with a short call (strike $X_2$ ). The third graph is the payoff diagram of a short call spread; it is just the mirror image in the $x$-axis of the long call spread.(ii) Put Spread (bear spread, capped put): This is completely analogous to the call spread just described. The corresponding diagrams are displayed in Figure 2.7.(iii) In glancing over the last two sets of graphs, the reader will notice that the short call spread and the put spread are very similar in form; so are the call spread and short put spread. How are they related?

## 金融代写|期权理论代写Mathematical Introduction to Options代考|COMBINATIONS BEFORE MATURITY

(i) The value of a combination of options before maturity is just equal to the sum of the values of the constituent simple options. The evolution of the value of a butterfly at times $T_1$ and $T_2$ before and at maturity is shown in Figure 2.12. Long before maturity, the curve of $f$ is featureless and only loosely acknowledges the direction of the asymptotic lines (see Section 2.3). As time passes, this curve begins to cling more and more tightly to the asymptotes, which are themselves moving towards the right. Finally, at maturity, the curve becomes the payoff diagram.

(ii) The curvature of $f$ is not uniform. In one region it is concave upwards (in the center); on either side it is convex downwards. Curvature is measured by a quantity called gamma; in the center, gamma is positive; on either side, it is negative.

The direction of the curvature remains fairly much the same as time elapses. However the sharpness of the curvature changes over time, becoming acute at the corners of the payoff diagram at maturity. Clearly, the size of gamma is related to how sharply the asymptotes change direction. In the center they turn through $90^{\circ}$ and gamma has the highest (positive) value. On either side, the asymptotes turn through $45^{\circ}$ and gamma has high (negative) values; at the edges they do not turn and gamma is small.
(iii) The rate at which the value of $f$ changes over time is known as theta. At the center of the butterfly, the curve of $f$ is moving downwards over time so that theta is negative; at the two edges the value is moving up so that theta is positive.

Some very significant observations can be made purely from the geometry of the graphs.

• At the center: gamma is at its largest and positive. Theta is negative and larger than anywhere else in the diagram. This part of the curve has to go all the way down to reach the bottom of the “V” by maturity.
• At the middle of the sloping sides: gamma is at its smallest since this is where it changes from positivé tó negativé. Théta is small sincê thé curvé for $f$ does nót havé tó move far to reach the asymptotes by maturity.
• At the top corners: gamma is negative and fairly large, although not as large as at the center. Theta is positive and fairly large again since the curve has quite a long way to travel to get into the corners by maturity.
• At the extreme edges: gamma is negative but small. Theta is positive and small.

# 期权理论代写

## 金融代写|期权理论代写Options数学介绍代考| Options组合选项

. . > .

(i)看涨价差(看涨价差，有上限的看涨期权):这是对看涨期权最简单的修改。其收益与看涨期权类似，不同之处在于它只会增加到一定水平，然后停止。之所以使用它，是因为期权发行者通常不愿意接受直接买入期权所产生的无限责任。收益图如图2.6的第一个图所示。重要的是要了解，欧洲呼叫价差(实际上是下面描述的任何组合)可以通过组合简单的选项来创建。图的第二张图 $2.6$ 显示看涨价差如何仅仅是一个长看涨(罢工)的组合 $X_1$ )和一个简短的呼吁(罢工 $X_2$ )。第三张图是卖空看涨价差的收益图;它只是一个镜像 $x$(ii)看跌期权价差(看跌价差，上限看跌期权):这与刚才描述的看涨期权价差完全类似。(iii)在浏览最后两组图表时，读者会注意到看涨期权价差和看跌期权价差在形式上非常相似;看涨期权价差和看跌期权价差也是如此。它们有什么关系?

## 金融代写|期权理论代写Options数学介绍代考| combination BEFORE MATURITY

.

(i)到期前的期权组合的值刚好等于组成该组合的简单期权的值之和。蝴蝶在成熟前$T_1$和$T_2$时刻的价值演变如图2.12所示。早在成熟之前，$f$的曲线是无特征的，只松散地承认渐近线的方向(见2.3节)。随着时间的推移，这条曲线开始越来越紧地附着在渐近线上，渐近线本身也在向右移动。最后，到期时，这条曲线变成了收益图

(ii) $f$的曲率是不均匀的。在一个区域上凹(在中心);两边都是向下凸的。曲率是由一个叫做伽马的量来衡量的;在中心，是正的;在任何一边，它都是负的。 随着时间的推移，曲率的方向基本保持不变。然而，曲率的锐度随着时间的推移而变化，在到期时收益图的角处变得锐。显然，的大小与渐近线改变方向的速度有关。在中间，他们转到$90^{\circ}$, gamma有最高的(正)值。在任意一边，渐近线通过$45^{\circ}$, gamma有高(负)值;
(iii) $f$的值随时间变化的速率称为theta。在蝴蝶的中心，曲线$f$随着时间向下移动，因此为负;在两条边的值向上移动，因此为正

• 在中心:伽马是最大的正的。是负的，比图中任何地方都大。曲线的这部分必须一直向下直到到期时达到V的底部。
• 在斜坡的中间:gamma是最小的，因为这是它从positivé tó negativé变化的地方。Théta是小的sincê thé curvé是$f$的nót havé tó在成熟时离渐近线很远吗?在顶部的角:伽玛是负的并且相当大，虽然没有在中心那么大。是正的，而且相当大因为曲线要经过很长一段路才能到达到期的拐角。
• 在极值边缘:gamma是负的但很小。

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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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