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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|Valuation of Pure Discount Bonds

Bonds represent specific claims to future cash flows. Like all financial securities, a bond’s value is the sum of the present value of its potential cash flows. A pure discount bond, also known as a zero coupon bond, offers a single future cash flow, usually depicted in textbooks for simplicity in a denomination such as $\$ 100, \$1,000$, or $\$ 10,000$, which is often referred to as the face value, principal, or par value. The time-to-receipt of a bond’s final cash flow is known as the time-to-maturity of the bond. The value of a$\$1,000$ (face value) pure discount bond with a maturity of five years is equal to $\$ 1,000$discounted for five years at a given or prevailing interest rate. Note that different issuers of bonds can have different levels of default risk, so the interest rates used to discount their promised cash flows to present value can be different. Denote the price of a$T$-year bond today as$B(0, T)$. The value or price,$B(0, T)$, of a pure discount bond given a continuously compounded market interest rate simply involves the application of Equation$2.6$(although the general case in Equation$2.7$also works) in which$T$represents the time-to-maturity in years and$F$is the face value or principal amount of the pure discount bond. $$B(0, T)=F \times e^{-r T}$$ Example 2.7: A two-year zero coupon bond pays a$\$100$ face value when two-year continuously compounded interest rates are $7.25 \%$. What is its price today?
Applying Equation $2.8$ generates:
$$B(0, T)=F \times e^{-r T}=\ 100 e^{-2 \times 0.0725}=\ 86.502$$
Alternatively, given the face value, $F$, and bond price $B(0, T)$ of a zero coupon bond, an analyst may compute the implied interest rate, which is called the T-year zero rate.

## 金融代写|金融数学代写Financial Mathematics代考|Coupon Bond Yields and Prices

We first assume that all bonds do not have default risk (i.e., they are riskfree bonds). Later in this section defaultable bonds are considered. Coupon bonds represent fixed claims to two types of cash flows: a series of equal payments referred to as coupons, $C$, and a final payment referred to as the principal amount or face value, $F$, of the bond. A coupon bond has a stated coupon rate (e.g., 7.375\%) that is distributed each year as a cash flow equal to the coupon rate times the bond’s principal value. The coupon rate on a particular bond is often set equal to market interest rates when a bond is initially issued so that the initial price of the bond will approximate its face value. The periodic coupon payments can then be viewed as regular payments of interest, unlike a zero coupon bond wherein an economic sense the payment of interest is deferred until maturity (and is distributed at maturity as the difference between the bond’s face value and its initial price).

The value of a $T$-year coupon bond, $B(0, T)$, can be viewed as the sum of the present values of an annuity (thee stream of coupons) and the preesent value of the principal or face value (a single cash flow). The formula for the present value of a coupon bond is shown in Equation 2.9. Note that the formula is simplified from Equation $2.7$ because all interest (coupon) payments $(C)$ are identical in a fixed rate bond and the bond’s last coupon, $C$, is combined with the principal or face value payment of $F$.
$$B(0, T)=C \sum_{i=1}^{n-1} e^{-r_{t_i} t_i}+(C+F) e^{-r_T T}$$
In practice, most coupon bonds pay coupons semiannually (at half the annual coupon rate). Equation $2.9$ is used assuming that $C$ represents a semiannual coupon payment, that $t_i$ is expressed in half-year intervals, that there are $n=2 T$ periods, and with $r_{t_i}$ denoting the corresponding market interest rate in each half-year period. The interest rate used for discount purposes is also called the discount rate. If the discount rate for each cash flow is equal to the market discount rate for the time-to-receipt of that cash flow, then the sum of the present values of each cash flow should equal the market price.

# 金融数学代考

## 金融代写|金融数学代写Financial Mathematics代考|纯贴现债券的估值

$$B(0, T)=F \times e^{-r T}=\ 100 e^{-2 \times 0.0725}=\ 86.502$$或者，给定面值， $F$，债券价格 $B(0, T)$ 对于零息债券，分析师可以计算隐含利率，称为t年零利率

## 金融代写|金融数学代写Financial Mathematics代考|券息债券收益率和价格

$T$年券息债券$B(0, T)$的价值可以被看作是年金的现值(一系列的券息)和本金或面值的现值(一个单一的现金流)的总和。息票债券现值的计算公式如式2.9所示。请注意，公式是由公式$2.7$简化的，因为在固定利率债券中，所有的利息(票面利率)支付$(C)$是相同的，债券的最后一个票面利率$C$与$F$的本金或面值支付结合在一起。
$$B(0, T)=C \sum_{i=1}^{n-1} e^{-r_{t_i} t_i}+(C+F) e^{-r_T T}$$

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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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