19th Ave New York, NY 95822, USA

金融代写|金融工程代考Financial Engineering代写|FIN323 Maturity-Independent Yields

my-assignmentexpert™提供最专业的一站式服务：Essay代写，Dissertation代写，Assignment代写，Paper代写，Proposal代写，Proposal代写，Literature Review代写，Online Course，Exam代考等等。my-assignmentexpert™专注为留学生提供Essay代写服务，拥有各个专业的博硕教师团队帮您代写，免费修改及辅导，保证成果完成的效率和质量。同时有多家检测平台帐号，包括Turnitin高级账户，检测论文不会留痕，写好后检测修改，放心可靠，经得起任何考验！

金融代写|金融工程代考Financial Engineering代写|Maturity-Independent Yields

The present value of a zero-coupon unit bond determines an interest rate called the yield and denoted by $y(0)$ to emphasise the fact that it is computed at time 0 :
$$B(0, N)=\mathrm{e}^{-N \tau y(0)} .$$
For a different running time instant $n$ such that $0<n<N$ the implied yield may in general be different from $y(0)$. For each such $n$ we thus have a number $y(n)$ satisfying
$$B(n, N)=\mathrm{e}^{-(N-n) \tau y(n)} .$$
Generally (and in most real cases), a bond with different maturity $N$ will imply a different yield. Nevertheless, in this section we consider the simplified situation when $y(n)$ is independent of $N$, that is, bonds with different maturities generate the same yield. Independence of maturity will be relaxed later in Section $10.2$.

金融代写|金融工程代考Financial Engineering代写|Investment in Single Bonds

If we invest in zero-coupon bonds and keep them to maturity, the rate of return is guaranteed, since the final payment is fixed in advance and is not affected by any future changes of interest rates. However, if we choose to close out our investment prior to maturity by selling the bonds, we face the risk that the interest rates may change in the meantime with an adverse effect on the final value of the investment.
Example $10.1$
Suppose we invest in bonds for a period of six months. Let $\tau=\frac{1}{12}$. We buy a number of unit bonds that will mature after one year, paying $B(0,12)=0.9300$ for each. This price implies a rate $y(0) \cong 7.26 \%$. Since we are going to sell the bonds at time $n=6$, we are concerned with the price $B(6,12)$ or, equivalently, with the corresponding rate $y(6)$. Let us discuss some possible scenarios:

1. The rate is stable, $y(6)=7.26 \%$. The bond price is $B(6,12) \cong 0.9644$ and the logarithmic return on the investment is $3.63 \%$, a half of the interest rate, in line with the additivity of logarithmic returns.
2. The rate decreases to $y(6)=6.26 \%$, say. (The convention is that $0.01 \%$ is one basis point, so here the rate drops by 100 basis points.) Then $B(6,12) \cong$ $0.9692$, which is more than in scenario 1 . As a result, we are going to earn more, achieving a logarithmic return of $4.13 \%$.
1. The rate increases to $y(6)=8.26 \%$. In this case the logarithmic return on our investment will be $3.13 \%$, which is lower than in scenario 1 , the bond price being $B(6,12) \cong 0.9596$.

金融代写|金融工程代考FINANCIAL ENGINEERING代 写|INVESTMENT IN SINGLE BONDS

$y(0) \cong 7.26 \%$. 因为我们要及时出售债券 $n=6$, 我们关心的是价格 $B(6,12)$ 或者，等效地，以相应的速率 $y(6)$. 让我们讨论一些可能的情况:
$B(6,12) \cong 0.9692$ ，这比方案 1 中的更多。结果，我们将赚取更多，实现对数回报 $4.13 \%$.

1. 速率增加到 $y(6)=8.26 \%$. 在这种情况下，我们投资的对数回报将是 $3.13 \%$ ，低于情景 1 ，债券价格为 $B(6,12) \cong 0.9596$.

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。