## 金融代写|利率建模代写Interest Rate Modeling代考|MATH5985

statistics-lab™ 为您的留学生涯保驾护航 在代写利率建模Interest Rate Modeling方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写利率建模Interest Rate Modeling代写方面经验极为丰富，各种代写利率建模Interest Rate Modeling相关的作业也就用不着说。

• 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|利率建模代写Interest Rate Modeling代考| A Binomial Tree for the Ho–Lee Model

The IIo-Lee model was first presented with a binomial tree. For a Gaussian short-rate model with mean and variance of change over $(t, t+\Delta t)$ given by
\begin{aligned} E^{\mathbb{Q}}\left[\Delta r_t\right] &=\theta_t \Delta t \ \operatorname{VaR}\left(\Delta r_t\right) &=\sigma^2 \Delta t \end{aligned}
we consider a rather natural binomial tree approximation as illustrated in Figure 5.1, where, without loss of generality, the branching probabilities are uniformly one half.
For notational efficiency, we let
$$r_{i, n}=r_{0,0}+\Delta t \sum_{k=1}^{n-1} \theta_k+(2 i-n) \sigma \sqrt{\Delta t}, \quad i=0,1, \ldots, n$$

Then we have a multi-period tree as shown in Figure 5.2.
Before being applied to derivatives pricing, such a tree must first be calibrated to the current term structure of the interest rate. For the Ho-Lee model, we need to determine the drift, $\theta_t$, by reproducing the prices of zero-coupon bonds of all maturities. This task can be efficiently achieved with the help of the so-called Arrow-Debreu prices.

## 金融代写|利率建模代写Interest Rate Modeling代考|Arrow–Debreu Prices

An Arrow-Debreu (1954) security is a canonical asset that has a cash flow of $\$ 1$if a particular state (of interest rate) is realized, or nothing otherwise. The pattern of payment is shown in Figure$5.3$, where we let$Q_{i, j}$denote the price of the security at time 0 that would pay$\$1$ at time $j$ if the state $i$ is realized, or nothing if otherwise.

Note that a zero-coupon bond can be regarded as a portfolio of ArrowDebreu securities. By linearity, the price of the zero-coupon bond maturing in time $j$ is equal to
$$P(0, j)=\sum_{i=0}^j Q_{i, j} .$$
Given an interest-rate tree as in Figure 5.2, we can construct the ArrowDebreu tree through a forward induction process. We begin with
$$Q_{0,0}=1 .$$
The calculations of $Q_{1,1}$ and $Q_{0,1}$ are done by “expectation pricing” using the trees in Figure $5.4$, where $r_{0,0}$ is the discount rate at node $(0,0)$. Intuitively, the prices of the two Arrow-Debreu securities are given by
$$Q_{1,1}=Q_{0,1}=\frac{1}{2} \mathrm{e}^{-r_{0,0} \Delta t}$$

## 金融代写|利率建模代写利率建模代考| Ho-Lee模型的二叉树

IIo-Lee模型首先用二叉树表示。对于均值和方差大于$(t, t+\Delta t)$的高斯短期速率模型(
\begin{aligned} E^{\mathbb{Q}}\left[\Delta r_t\right] &=\theta_t \Delta t \ \operatorname{VaR}\left(\Delta r_t\right) &=\sigma^2 \Delta t \end{aligned}
)，我们考虑一种相当自然的二叉树近似，如图5.1所示，在不丧失一般性的情况下，分支概率一致为1 / 2。

$$r_{i, n}=r_{0,0}+\Delta t \sum_{k=1}^{n-1} \theta_k+(2 i-n) \sigma \sqrt{\Delta t}, \quad i=0,1, \ldots, n$$

## 金融代写|利率建模代写Interest Rate Modeling代考| 阿罗-德布鲁·普莱斯

a Arrow-Debreu(1954)证券是一种典型资产，如果实现了特定的(利率)状态，或者其他什么都没有，那么它的现金流为$\$ 1$。支付模式如图$5.3$所示，其中我们让$Q_{i, j}$表示时间0时的证券价格，如果状态$i$实现，则在时间$j$时支付$\$1$，否则则不支付

$$P(0, j)=\sum_{i=0}^j Q_{i, j} .$$

$$Q_{0,0}=1 .$$

$$Q_{1,1}=Q_{0,1}=\frac{1}{2} \mathrm{e}^{-r_{0,0} \Delta t}$$ 给出

## 有限元方法代写

tatistics-lab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。

## 金融代写|利率建模代写Interest Rate Modeling代考|ACTL40004

statistics-lab™ 为您的留学生涯保驾护航 在代写利率建模Interest Rate Modeling方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写利率建模Interest Rate Modeling代写方面经验极为丰富，各种代写利率建模Interest Rate Modeling相关的作业也就用不着说。

• 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|利率建模代写Interest Rate Modeling代考| GENERAL MARKOVIAN MODELS

Existing short-rate models are Markovian models. A no-arbitrage shortrate model should also be derived from the HJM framework. However, this can be quite difficult. In this section, we address the opposite question: under what kind of forward-rate volatility specifications should the resulting short-rate model be a Markovian random variable? Answering this question will help us to calibrate and implement a short-rate model more efficiently.
According to Equation 4.21, the short rate can be expressed as
$$r_t=f(t, t)=f(0, t)+\int_0^t\left[-\boldsymbol{\sigma}^{\mathrm{T}}(s, t) \mathbf{\Sigma}(s, t) \mathrm{d} s+\boldsymbol{\sigma}^{\mathrm{T}}(s, t) \mathrm{d} \mathbf{W}_s\right]$$

where $\mathbf{W}t$ is the $n$-dimensional Brownian motion under the risk-neutral measure, $\sigma(t, T)$ the forward-rate volatility, and $\boldsymbol{\Sigma}(t, T)$ the volatility of the $T$-maturity zero-coupon bond, given by $\boldsymbol{\Sigma}(t, T)=-\int_t^T \boldsymbol{\sigma}(t, u) \mathrm{d} u$. The stochastic differentiation of the short rate is \begin{aligned} \mathrm{d} r_t=& {\left[f_t(0, t)+\int_0^t\left(-\frac{\partial}{\partial t}\left(\boldsymbol{\sigma}^{\mathrm{T}}(s, t) \boldsymbol{\Sigma}(s, t)\right) \mathrm{d} s+\frac{\partial \boldsymbol{\sigma}^{\mathrm{T}}(s, t)}{\partial t} \mathrm{~d} \mathbf{W}_s\right)\right] \mathrm{d} t } \ &+\boldsymbol{\sigma}^{\mathrm{T}}(t, t) \mathrm{d} \mathbf{W}_t \ =& {\left[f_t(t, T)\right]{T=t} \mathrm{~d} t+\boldsymbol{\sigma}^{\mathrm{T}}(t, t) \mathrm{d}t . } \end{aligned} Based on Equation $5.17$ we can make the following judgment: for the shortrate model to be a Markovian process, we need the drift term, $\left[f_t(t, T)\right]{T=t}$, to be a function of a finite set of state variables that are jointly Markovian in their evolution.

To write the short rate as a function of several state variables, we introduce auxiliary functions
$$b_i(t, T)=\sigma_i(t, T) \int_t^T \sigma_i(t, s) \mathrm{d} s, \quad i=1,2, \ldots, n .$$

## 金融代写|利率建模代写Interest Rate Modeling代考|Monte Carlo Simulations for Options Pricing

Owing to the Markovian property of short-rate models, path simulations by Monte Carlo methods can be carried out efficiently, which is important for pricing exotic and path-dependent options. Take the pricing of the option on a zero-coupon for example. The value can be expressed as
$$V_t=E_t^{\mathbb{Q}}\left[\mathrm{e}^{-\int_t^T r_s \mathrm{~d} s}(P(T, \tau)-K)^{+}\right], \quad t<T<\tau$$
where $\mathbb{Q}$ stands for the risk-neutral measure, $r_t$ is given by Equation $5.20$, and the bond price is given by Equation 5.39. Both variables are expressed in terms of $\chi_i(t)$ and $\varphi_i(t), i=1, \ldots, n$, which evolve according to Equation 5.23. The corresponding simulation scheme for $\chi_i(t)$ and $\varphi_i(t)$ is
\begin{aligned} &\varphi_i(t+\Delta t)-\varphi_i(t)+\left(\sigma_i^2(t, t)-2 \kappa_i(t) \varphi_i(t)\right) \Delta t \ &\chi_i(t+\Delta t)=\chi_i(t)+\left(\varphi_i(t)-\kappa_i(t) \chi_i(t)\right) \mathrm{d} t+\sigma_i(t, t) \Delta W_i(t) \end{aligned}
which is simply the so-called Euler scheme. The bond option is priced by simulating many payoffs before taking an average.
In Inui and Kijima (1998), the following example is considered:
$$\boldsymbol{\sigma}(t, T)=\left(\begin{array}{c} c_1 r_t^\alpha \ c_2 r_t^\beta \mathrm{e}^{-\kappa(T-t)} \end{array}\right)$$
where $c_i, i=1,2, \alpha, \beta$, and $\kappa$ are non-negative constants. It can be verified that the components of the volatility vector satisfy
$$\frac{\partial \sigma_1(t, T)}{\partial T}=0, \quad \frac{\partial \sigma_2(t, T)}{\partial T}=-\kappa \sigma_2(t, T) .$$

## 金融代写|利率建模代写Interest Rate Modeling代考| 一般马尔可夫模型

$$r_t=f(t, t)=f(0, t)+\int_0^t\left[-\boldsymbol{\sigma}^{\mathrm{T}}(s, t) \mathbf{\Sigma}(s, t) \mathrm{d} s+\boldsymbol{\sigma}^{\mathrm{T}}(s, t) \mathrm{d} \mathbf{W}_s\right]$$

where $\mathbf{W}t$ 是 $n$风险中性测度下的-维布朗运动， $\sigma(t, T)$ 远期利率波动 $\boldsymbol{\Sigma}(t, T)$ 波动率 $T$到期零息债券，由 $\boldsymbol{\Sigma}(t, T)=-\int_t^T \boldsymbol{\sigma}(t, u) \mathrm{d} u$。短期汇率的随机微分是 \begin{aligned} \mathrm{d} r_t=& {\left[f_t(0, t)+\int_0^t\left(-\frac{\partial}{\partial t}\left(\boldsymbol{\sigma}^{\mathrm{T}}(s, t) \boldsymbol{\Sigma}(s, t)\right) \mathrm{d} s+\frac{\partial \boldsymbol{\sigma}^{\mathrm{T}}(s, t)}{\partial t} \mathrm{~d} \mathbf{W}_s\right)\right] \mathrm{d} t } \ &+\boldsymbol{\sigma}^{\mathrm{T}}(t, t) \mathrm{d} \mathbf{W}_t \ =& {\left[f_t(t, T)\right]{T=t} \mathrm{~d} t+\boldsymbol{\sigma}^{\mathrm{T}}(t, t) \mathrm{d}t . } \end{aligned} 基于方程 $5.17$ 我们可以做出以下判断:要使短期模型为马尔可夫过程，我们需要漂移项， $\left[f_t(t, T)\right]{T=t}$，是一组有限状态变量的函数，这些状态变量在演化过程中共同具有马尔可夫性 为了将短期汇率写成几个状态变量的函数，我们引入了辅助函数
$$b_i(t, T)=\sigma_i(t, T) \int_t^T \sigma_i(t, s) \mathrm{d} s, \quad i=1,2, \ldots, n .$$

## 金融代写|利率建模代写利率建模代考|期权定价的蒙特卡洛模拟

$$V_t=E_t^{\mathbb{Q}}\left[\mathrm{e}^{-\int_t^T r_s \mathrm{~d} s}(P(T, \tau)-K)^{+}\right], \quad t<T<\tau$$
，其中$\mathbb{Q}$表示风险中性测度，$r_t$由式$5.20$给出，债券价格由式5.39给出。两个变量都用$\chi_i(t)$和$\varphi_i(t), i=1, \ldots, n$表示，根据公式5.23进行演化。$\chi_i(t)$和$\varphi_i(t)$对应的模拟方案是
\begin{aligned} &\varphi_i(t+\Delta t)-\varphi_i(t)+\left(\sigma_i^2(t, t)-2 \kappa_i(t) \varphi_i(t)\right) \Delta t \ &\chi_i(t+\Delta t)=\chi_i(t)+\left(\varphi_i(t)-\kappa_i(t) \chi_i(t)\right) \mathrm{d} t+\sigma_i(t, t) \Delta W_i(t) \end{aligned}
，这就是所谓的欧拉方案。债券期权的定价是通过在取平均值之前模拟许多支付进行的。在Inui和Kijima(1998)中，考虑以下例子:
$$\boldsymbol{\sigma}(t, T)=\left(\begin{array}{c} c_1 r_t^\alpha \ c_2 r_t^\beta \mathrm{e}^{-\kappa(T-t)} \end{array}\right)$$

$$\frac{\partial \sigma_1(t, T)}{\partial T}=0, \quad \frac{\partial \sigma_2(t, T)}{\partial T}=-\kappa \sigma_2(t, T) .$$

## 有限元方法代写

tatistics-lab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。

## 金融代写|利率建模代写Interest Rate Modeling代考|ACTL90003

statistics-lab™ 为您的留学生涯保驾护航 在代写利率建模Interest Rate Modeling方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写利率建模Interest Rate Modeling代写方面经验极为丰富，各种代写利率建模Interest Rate Modeling相关的作业也就用不着说。

• 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|利率建模代写Interest Rate Modeling代考| ON THE LOGNORMAL SPECIFICATION OF FORWARD RATES

We now explore the possibility of using the state-dependent volatility function in the HJM model. Without loss of generality, we consider the forward-rate volatility function of the form
$$\sigma(t, T)=\sigma_0(t, T) f^\alpha(t, T),$$

where $\sigma_0(t, T)$ is a deterministic function and $\alpha$ a positive exponent. In the special case, $\alpha=0$, we obtain a Gaussian model.

Similar to Avellaneda and Laurence (1999), we show that the “lognormal” model, corresponding to $\alpha=1$, blows up in finite time in the sense that a forward rate reaches infinity. This result was first obtained by Morton (1988). One can imagine that similar results may apply to the case of $\alpha>0$. Hence, volatility specification in the form of Equation $4.136$ is denied.

It suffices to show the result with a one-factor model. The no-arbitrage condition dictates that the drift must be
$$\mu(t, T)=f(t, T) \sigma_0(t, T) \int_t^T f(t, s) \sigma_0(t, s) \mathrm{d} s,$$
which depends on the entire curve of $f(t, s), t \leq s \leq T$. Consider the simplest specification of $\sigma_0(t, T)$ : $\sigma_0(t, T)=\sigma_0=$ constant. The HJM equation then becomes
$$\frac{\mathrm{d} f(t, T)}{f(t, T)}=\sigma_0 \mathrm{~d} \tilde{W}_t+\left(\sigma_0^2 \int_t^T f(t, s) \mathrm{d} s\right) \mathrm{d} t .$$
The formal solution to the above equation is
\begin{aligned} f(t, T) &=f(0, T) \exp \left(\sigma_0 \tilde{W}_t-\frac{\sigma_0^2}{2} t+\sigma_0^2 \int_0^t\left(\int_s^T f(s, u) \mathrm{d} u\right) \mathrm{d} s\right) \ &=f(0, T) M(t) \exp \left(\sigma_0^2 \int_0^t\left(\int_s^T f(s, u) \mathrm{d} u\right) \mathrm{d} s\right) \end{aligned} where $M(t)=\exp \left(\sigma_0 \tilde{W}_t-\left(\sigma_0^2 / 2\right) t\right)$. Assume for simplicity that the initial term structure is flat, that is, $f(0, T)=f_0=$ constant.

## 金融代写|利率建模代写Interest Rate Modeling代考|FROM SHORT-RATE MODELS TO FORWARD-RATE MODELS

Short-rate models dominated fixed-income modeling before the emergence of the no-arbitrage framework of Heath, Jarrow, and Morton (1992), which is based on forward rates. Short-rate models can be made arbitrage free by taking appropriate drift terms, such as the Ho-Lee model and the I Iull-White model. But this is not always easy. One way to derive the correct drift term is to identify the corresponding forward-rate volatility and then to solve for the expression of the forward rates, which include the short rate as an extreme case, from the HJM equation. The focus in this section is on how to derive the corresponding forward-rate volatility in order to identify the model as a special case of the HJM framework.

Consider in general an Ito’s process for the short rate under the riskneutral measure, $\mathbb{Q}$,
$$\mathrm{d} r_t=v\left(r_t, t\right) \mathrm{d} t+\rho\left(r_t, t\right) \mathrm{d} W_t,$$ where the drift, $v\left(r_t, t\right)$, and volatility, $\rho\left(r_t, t\right)$, are deterministic functions of their arguments. Note that, for notational simplicity, we hereafter drop ” $\sim$ ” over the $\mathbb{Q}$-Brownian motion, $W_t$. Define an auxiliary function
$$g(x, t, T)=-\ln E^{\mathbb{Q}}\left[\exp \left(-\int_t^T r_s \mathrm{~d} s\right) \mid r_t=x\right]$$
We have the following result (Baxter and Rennie, 1996).

## 金融代写|利率建模代写Interest Rate Modeling代考| 关于远期汇率的对数正规规范

$$\sigma(t, T)=\sigma_0(t, T) f^\alpha(t, T),$$

$$\mu(t, T)=f(t, T) \sigma_0(t, T) \int_t^T f(t, s) \sigma_0(t, s) \mathrm{d} s,$$
，这取决于$f(t, s), t \leq s \leq T$的整条曲线。考虑$\sigma_0(t, T)$: $\sigma_0(t, T)=\sigma_0=$常量的最简单规范。HJM方程于是变成
$$\frac{\mathrm{d} f(t, T)}{f(t, T)}=\sigma_0 \mathrm{~d} \tilde{W}_t+\left(\sigma_0^2 \int_t^T f(t, s) \mathrm{d} s\right) \mathrm{d} t .$$

\begin{aligned} f(t, T) &=f(0, T) \exp \left(\sigma_0 \tilde{W}_t-\frac{\sigma_0^2}{2} t+\sigma_0^2 \int_0^t\left(\int_s^T f(s, u) \mathrm{d} u\right) \mathrm{d} s\right) \ &=f(0, T) M(t) \exp \left(\sigma_0^2 \int_0^t\left(\int_s^T f(s, u) \mathrm{d} u\right) \mathrm{d} s\right) \end{aligned}，其中$M(t)=\exp \left(\sigma_0 \tilde{W}_t-\left(\sigma_0^2 / 2\right) t\right)$。为简单起见，假设初始期限结构是平坦的，即$f(0, T)=f_0=$常数。

## 金融代写|利率建模代写Interest Rate Modeling代考|从短期利率模型到远期利率模型

$$\mathrm{d} r_t=v\left(r_t, t\right) \mathrm{d} t+\rho\left(r_t, t\right) \mathrm{d} W_t,$$，其中漂移，$v\left(r_t, t\right)$和波动率，$\rho\left(r_t, t\right)$是其参数的确定性函数。注意，为了表示法的简单性，我们以后在$\mathbb{Q}$ -布朗运动$W_t$上省略“$\sim$”。定义一个辅助函数
$$g(x, t, T)=-\ln E^{\mathbb{Q}}\left[\exp \left(-\int_t^T r_s \mathrm{~d} s\right) \mid r_t=x\right]$$

## 有限元方法代写

tatistics-lab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。

## 金融代写|金融数学代写Financial Mathematics代考|MATH3090

statistics-lab™ 为您的留学生涯保驾护航 在代写金融数学Financial Mathematics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写金融数学Financial Mathematics代写方面经验极为丰富，各种代写金融数学Financial Mathematics相关的作业也就用不着说。

• 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|The Limits to Arbitrage and Complete Markets

The models and intuition of earlier sections often relied on or described prices in frictionless markets wherein numerous investors such as speculators and arbitragers compete to earn higher returns. Financial economists often describe this condition of informational market efficiency as being when all available information becomes reflected in market prices such that it is not possible to utilize that information to consistently earn a riskadjusted abnormal profit (i.e., market participants cannot consistently identify mispriced securities).
A well-recognized problem with the theory of informationally efficient markets is that if available information is instantaneously incorporated into market prices then there will be no incentive for market participants to gather information and integrate that information into their investment decisions. If no one searches for mispriced securities then prices will not be efficient. In a perfectly efficient market everyone would adopt passive investment strategies which are buy-and-hold strategies with no attempt to trade in an effort to gain from mispriced securities.
Clearly no market can be perfectly efficient. The only meaningful issue is the extent to which markets approach informational efficiency.

The concept of inefficiently efficient markets is that securities are mispriced just enough and just often enough to attract a moderate number of active investment managers (managers that execute trades for the purpose of trying to improve risk-adjusted return) and active individual investors. The benefits and costs of active investing reach an equilibrium that results in a level of market inefficiency that sustains this equilibrium level of information analysis.

The primary purpose of derivatives is to facilitate risk management. Financial derivatives help to complete a market. Perfect completion of a market means that there are enough distinct investment opportunities available that investors can establish long and short positions in existing securities in a way that allows them to position their portfolio exactly as they desire. As an example, if a grocery store mixes apples, bananas, and cherries into three different types of fruit baskets, a customer may be inconvenienced by being unable to purchase one basket with exactly the amount of each type of fruit that she desires unless by chance one of the baskets exactly meets her preferences. However, if a customer is allowed to trade with the store and can buy and sell the different types of fruit baskets without trading costs, she will be able to obtain exactly the numbers of each type of fruit that she desires so long as the number of distinct fruit baskets being traded equals the number of different types of fruit (i.e., the market is complete). In a similar way, derivatives are created to move the market closer to completion so that market participants are better able to establish positions that move the participants closer to their desired risk exposures.
Financial derivatives can also be used to provide arbitragers, speculators, and investors with powerful tools with which to attempt to enhance their risk-adjusted returns through superior processing of available information. When those market participants with the greatest abilities to identify mispriced securities are enabled with superior tools such as derivatives to best utilize their abilities to buy underpriced assets and sell overpriced assets, the market prices of assets will tend to be better driven toward their intrinsic values. Because market prices provide the signals that guide production and consumption decisions throughout an economy, these arbitragers, speculators, and investors are unwittingly driving the decision making throughout the entire economy into being more and more efficient. Therefore, derivatives can play a role in increasing the efficiency in production and consumption decisions which in turn means improved economic growth and economic utility.

## 金融代写|金融数学代写Financial Mathematics代考|Chapter Demonstrating Exercises

A U.S.-based export firm will receive 10 million British pounds in three months. The firm can tolerate an exchange rate between $\$ 1.25$to$\$1.34$ U.S. dollars per pound to convert the pounds to its domestic currency (U.S. dollars), but is unwilling to bear the risk of converting the foreign exchange to U.S. dollars at an exchange rate of $\$ 1.25$or lower. On the other hand, the firm will be very content with an exchange rate of$\$1.34$ per British pound. How can a financial derivative strategy be designed to meet the needs of this U.S. export firm?
Payoff in upstate $=\$ 16=$bond$+(h \times$call$)=\$7+(h \times \$ 3)$$$h=(\ 16-\ 7) / \ 3=3$$ ## 金融代写|金融数学代写Financial Mathematics代考|Popular Option Strategies with Multiple Positions Two of the most popular strategies involving options are covered calls and protective puts. Both of these strategies were illustrated in the examples in Section 1.5.1. A covered call is the simultaneous writing of a call option while having a long position in the underlying asset. A protective put is the simultaneous purchase of a put option while having a long position in the underlying asset. These two portfolios are depicted in Figure$1.8$and Figure$1.9$Note that the portfolio profits and losses in Figures$1.8$and$1.9$can be formed by summing the profits and losses of the portfolio’s component positions. In other words, at each point on the horizontal axis (i.e., each value of$S_T$), the profit or loss of the covered call or protective put is found by summing the profits and/or losses of the two positions that form them. Option spreads are simultaneous long and short positions in either different call options or different put options (but not both calls and puts). Three general types of option spread strategies are vertical spreads, horizontal spreads, and diagonal spreads. The terms describing the three spreads relate to the visualization of a matrix of option prices with strike price forming the vertical axis and expiration date forming the horizontal axis. Thus, in a vertical option spread, the options differ by strike price; in a horizontal option spread, the options differ by expiration date; and in a diagonal spread, they differ by both strike price and expiration date. This section focuses on the strategies with the same expiration date – vertical spreads. Figure$1.10$illustrates a vertical call spread known as a bull spread. The payout of a bull spread at expiration is positively related to the underlying asset, hence it is “bullish” with respect to the price of the underlying asset. The bullish nature of a bull spread occurs when the long call option position is in the option with the lower strike price and the short option position is in the asset with the higher strike price. Interestingly, the same bullish diagram can be generated using put options with the same structure: the long put option position is in the option with the lower strike price and the short option position is in the asset with the higher strike price. Figure$1.11$illustrates a vertical call spread known as a bear spread. Bear spreads reverse the direction of the options by establishing the long call option position in the option with the higher strike price and the short option position is in the asset with the lower strike price. Like in the case of bull spreads, the same bearish diagram can be generated using put options with the same structure: the long put option position is in the option with the higher strike price and the short option position is in the asset with the lower strike price. ## 金融数学代考 ## 金融代写|金融数学代写金融数学代考|无套利二项期权估值 无套利衍生品估值最吸引人的模型之一是二项期权定价模型。二项模型只允许一股股票在一段时间内的价值产生两种可能的结果。每种可能的结果都被称为“状态”，通常被描述为“向上状态”或“向下状态”。例如，考虑一股目前交易价格为每股$\$10$的股票，它被认为在一年底有两种可能的结果:如果情况顺利(上升状态)，它的价格为$\$ 16$;如果情况不顺利(下降状态)，它的价格为$\$7$。我们将股票的当前价格表示为$S_0$，将处于上涨状态的股价值表示为$S_u$，将处于下跌状态的股票值表示为$S_d$。图$1.6$说明了所有二项模型中最简单的一个时间段。现在考虑这只股票的看涨期权，在一个时期内到期，执行价为$\$ 13$。虽然我们还不知道该期权的市场价值$C_0$，但我们确实知道该期权在年底的价值($C_u$在上升状态，$C_d$在下降状态)从$\$3$在上升状态(发现为$\$ 16-\$13$)和$\$ 0$在下降状态(因为该期权没有被执行)的支付，如图1.7所示 注意，股票价格在两种状态(即$\$16-\$ 7$)之间的变化是$\$9$，而与此同时，期权价格只变化$\$ 3$。解决当前期权价格$\left(C_0\right)$的关键是要意识到期权的收益与股票的收益是完全相关的。唯一的区别是股价的变化是三倍，股价的最坏情况值是$\$7$，而期权的最坏情况值是$\$ 0$。这意味着一个套利者可以构建两个具有相同收益的投资组合，这被称为用一个投资组合复制另一个投资组合。这里，我们构建了两个投资组合:(1)一个或多个看涨期权加上一个无风险债券和(2)一股股票。这两种投资组合在期权到期时的收益是相同的。如果它们的收益相同，那么它们的现值也一定相同。用看涨期权和债券来复制股票，收益必须是相同的。第一步是要注意，如果期权到期时毫无价值，无风险债券的支付必须与下跌状态下的股票相同(在这种情况下是$\$7)$)。因此，无风险债券的面值必须为$\$ 7$。第二步是确定看涨期权的数量，这些看涨期权与债券相结合，在期权到期时提供的股息与北部州的股票(16美元)相同。看涨期权的数量$h$必须满足以下条件: 在上州的偿付$=\$16=$ bond $+(h \times$ call $)=\$ 7+(h \times \$3)$
$$h=(\ 16-\ 7) / \ 3=3$$

## 有限元方法代写

tatistics-lab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。

## 统计代写|金融统计代写Financial Statistics代考|AEM4070

statistics-lab™ 为您的留学生涯保驾护航 在代写金融统计Financial Statistics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写金融统计Financial Statistics代写方面经验极为丰富，各种代写金融统计Financial Statistics相关的作业也就用不着说。

• 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

## 统计代写|金融统计代写Financial Statistics代考|Data Presentation: Tables

All data tables have four elements: a caption, column labels, row labels, and cells. The caption describes the information that is contained in the table. The column labels identify the information in the columns, such as the gross national product, the inflation rate, or the Dow Jones Industrial Average. Examples of row labels include years, dates, and states. A cell is defined by the intersection of a specific row and a specific column.

Example 2.2 Annual CPI, T-Bill Rate, and Prime Rate. To illustrate, Table $2.1$ gives some macroeconomic information from 1950 to 2010 . The caption is “CPI, T-bill rate, and prime rate (1950-2010).” The row labels are the years 1950-2010. The column labels are CPI (consumer pace index), 3-month T-bill rate, and prime rate. Changes in the consumer price index, the most commonly used indicator of the economy’s price level, are a measure of inflation or deflation. (For a more detailed description of the CPI, see Chap. 19.) The 3-month T-bill interest rate is the interest rate that the USA Treasury pays on 91-day debt instruments, and the prime rate is the interest rate that banks charge on loans to their best customers, usually large firms. This table, then, presents macroeconomic information for any year indicated. For example, the CPI for 2010 was $218.1$ and the prime rate in 2008 was $5.09 \%$. The relationship between the CPI and 3-month T-bill rate will be discussed in Chap. $19 .$

## 统计代写|金融统计代写Financial Statistics代考|Data Presentation: Charts and Graphs

It is sometimes said that a picture is worth a thousand words, and nowhere is this statement more true than in the analysis of data. Tables are usually filled with highly specific data that take time to digest. Graphs and charts, though they are often less detailed than tables, have the advantage of presenting data in a more accessible and memorable form. In most graphs and charts, the independent variable is plotted on the horizontal axis (the $x$-axis) and the dependent variable on the vertical axis (the $y$-axis). Frequently, “time” is plotted along the $x$-axis. Such a graph is known as a time-series graph because on it, changes in a dependent variable (such as GDP, inflation rate, or stock prices) can be traced over time.

Line charts are constructed by graphing data points and drawing lines to connect the points. Figure $2.1$ shows how the rate of return on the S\&P 500 and the 3-month T-bill rate have varied over time. ${ }^1$ The independent variable is the year (ranging from 1990 to 2010), so this is a time-series graph. The dependent variables are often in percentages.

Figure $2.2$ is a graph of the components of the gross domestic product (GDP)personal consumption, government expenditures, private investment, and net exports-over time. This is also a time-series graph because the independent variable is time. It is a component-parts line chart. These series have been “deflated” by expressing dollar amounts in constant 2005 dollars. (Chap. 19 discusses the deflated series in further detail.)

Figure $2.2$ is also called a component-parts line graph because the four parts of the GDP are graphed. The sum of the four components equals the GDP. Using this type of graph makes it possible to show the sources of increases or declines in the GDP. (The data used to generate Fig. $2.2$ are found in Table 2.2.)

Bar charts can be used to summarize small amounts of information. Figure $2.3$ shows the average annual returns for Tri-Continental Corporation for investment periods of seven different durations ending on September 30, 1991. This figure shows that Tri-Continental has provided investors double-digit returns during a 50-year period.

It also shows that the investment performance of this company was better than that of the Dow Jones Industrial Average (DJIA) and the S\&P $500 .^2$

## 有限元方法代写

tatistics-lab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。

## 统计代写|金融统计代写Financial Statistics代考|GRA6518

statistics-lab™ 为您的留学生涯保驾护航 在代写金融统计Financial Statistics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写金融统计Financial Statistics代写方面经验极为丰富，各种代写金融统计Financial Statistics相关的作业也就用不着说。

• 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

## 统计代写|金融统计代写Financial Statistics代考|Deductive Versus Inductive Analysis in Statistics

We also encounter another dichotomy in statistical analysis. Deduction is the use of general information to draw conclusions about specific cases. For example, probability tells us that if a student is chosen by lottery from a calculus class composed of 60 mathematics majors and 40 business administration majors, then the odds against picking a mathematics majors are 4-6. Thus we can deduce that about $40 \%$ of such single-member samples of the students in this calculus class will be business administration majors. As another example of deduction, consider a firm that learns that $1 \%$ of its auto parts are defective and concludes that in any random sample, $1 \%$ of its parts are therefore going to be defective. The use of probability to determine the chance of obtaining a particular kind of sample result is known as deductive statistical analysis.
In Chaps. 5, 6, and 7, we will learn how to apply deductive techniques when we know everything about the population in advance and are concerned with studying the characteristics of the possible samples that may arise from that known population.
Induction involves drawing general conclusions from specific information. In statistics, this means that on the strength of a specific sample, we infer something about a general population. The sample is all that is known; we must determine the uncertain characteristics of the population from the incomplete information available. This kind of statistical analysis is called inductive statistical analysis. For example, if $56 \%$ of a sample prefers a particular candidate for a political office, then we can estimate that $56 \%$ of the population prefers this candidate. Of course, our estimate is subject to error, and statistics enables us to calculate the possible error of an estimate. In this example, if the error is $3 \%$ points, it can be inferred that the actual percentage of voters preferring the candidate is $56 \%$ plus or minus $3 \%$; that is, it is between $53 \%$ and $59 \%$.

Deductive statistical analysis shows how samples are generated from a population, and inductive statistical analysis shows how samples can be used to infer the characteristics of a population. Inductive and deductive statistical analyses are fully complementary. We must study how samples are generated before we can learn to generalize from a sample.

## 统计代写|金融统计代写Financial Statistics代考|Data Collection

After identifying a research problem and selecting the appropriate statistical methodology, researchers must collect the data that they will then go on to analyze. There are two sources of data: primary and secondary sources. Primary data are data collected specifically for the study in question. Primary data may be collected by methods such as personal investigation or mail questionnaires. In contrast, secondary data were not originally collected for the specific purpose of the study at hand but rather for some other purpose. Examples of secondary sources used in finance and accounting include the Wall Street Journal, Barron’s, Value Line Investment Survey, Financial Times, and company annual reports. Secondary sources used in marketing include sales reports and other publications. Although the data provided in these publications can be used in statistical analysis, they were not specifically collected for that use in any particular study.

Example 2.1 Primary and Secondary Sources of Data. Let us consider the following cases and then characterize each data source as primary or secondary:

1. (Finance) To determine whether airline deregulation has increased the return and risk of stocks issued by firms in the industry, a researcher collects stock data from the Wall Street Journal and the Compustat database. (The Compustat database contains accounting and financial information for many firms.)
2. (Production) To determine whether ball bearings meet measurement specifications, a production engineer examines a sample of 100 bearings.
3. (Marketing) Before introducing a hamburger made with a new recipe, a firm gives 25 customers the new hamburger and asks them on a questionnaire to rate the hamburger in various categories.
4. (Political science) A candidate for political office has staff members call 1,000 voters to determine what candidate they prefer in an upcoming election.
5. (Marketing) A marketing firm looks up, in Consumer Reports, the demand for different types of cars in the United States.

## 统计代写|金融统计代写Financial Statistics代考|Data Collection

1. （金融）为了确定航空公司放松管制是否增加了行业公司发行股票的回报和风险，研究人员从华尔街日报和 Compustat 数据库收集股票数据。（Compustat 数据库包含许多公司的会计和财务信息。）
2. （生产）为了确定滚珠轴承是否符合测量规格，生产工程师检查了 100 个轴承样本。
3. （营销）在推出使用新配方制作的汉堡包之前，一家公司向 25 位顾客提供了新汉堡包，并要求他们在问卷上对不同类别的汉堡包进行评分。
4. （政治学）政治职位候选人让工作人员召集 1,000 名选民，以确定他们在即将到来的选举中更喜欢哪位候选人。
5. （营销）一家营销公司在《消费者报告》中查找了美国对不同类型汽车的需求。

## 有限元方法代写

tatistics-lab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。

## 统计代写|金融统计代写Financial Statistics代考|ST326

statistics-lab™ 为您的留学生涯保驾护航 在代写金融统计Financial Statistics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写金融统计Financial Statistics代写方面经验极为丰富，各种代写金融统计Financial Statistics相关的作业也就用不着说。

• 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

## 统计代写|金融统计代写Financial Statistics代考|The Role of Statistics in Business and Economics

Statistics is a body of knowledge that is useful for collecting, organizing, presenting, analyzing, and interpreting data (collections of any number of related observations) and numerical facts. Applied statistical analysis helps business managers and economic planners formulate management policy and make business decisions more effectively. And statistics is an important tool for students of business and economics. Indeed, business and economic statistics has become one of the most important courses in business education, because a background in applied statistics is a key ingredient in understanding accounting, economics, finance, marketing, production, organizational behavior, and other business courses.

We may not realize it, but we deal with and interpret statistics every day. For example, the Dow Jones Industrial Average (DJIA) is the best-known and most widely watched indicator of the direction in which stock market values are heading. When people say, “The market was up 12 points today,” they are probably referring to the DJIA. This single statistic summarizes stock prices of 30 large companies. Rather than listing the prices at which all of the approximately 2,000 stocks traded on the New York Stock Exchange are currently selling, analysts and reporters often cite this one number as a measure of overall market performance.

Let’s take another example. Before elections, the media sometimes present surveys of voter preference in which a sample of voters instead of the whole population of voters is asked about candidate preferences. The media usually give the results of the poll and then state the possible margin of error. A margin of error of $3 \%$ means that the actual extent of a candidate’s popular support may differ from the poll results by as much as $3 \%$ points in either direction (“plus or minus”). Anyone who conducts a survey must understand statistics in order to make such decisions as how many people to contact, how to word the survey, and how to calculate the potential margin of error.

In business and industry, managers frequently use statistics to help them make better decisions. A shoe manufacturer, for instance, needs to produce a forecast of future sales in order to decide whether to expand production. Sales forecasts provide statistical guidance in most business decision making.

On a broader scale, the government publishes a variety of data on the health of the economy. Some of the most popular measures are the gross national product (GNP), the index of leading economic indicators, the unemployment rate, the money supply, and the consumer price index (CPI). All these measures are statistics that are used to summarize the general state of the economy. And, of course, business, government, and academic economists use statistical methods to try to predict these macroeconomic and other variables.

The following additional examples are presented to show that the use of statistics is widespread not only in business and economics but in everyday life as well.

## 统计代写|金融统计代写Financial Statistics代考|Descriptive Versus Inferential Statistics

Having gotten a feel for the use of statistics by looking at several illustrations, we can now refine our definition of the term. Statistics is the collection, presentation, and summary of numerical information in such a way that the data can be easily interpreted.

There are two basic types of statistics: descriptive and inferential. Descriptive statistics deals with the presentation and organization of data. Measures of central tendency, such as the mean and median, and measures of dispersion, such as the standard deviation and range, are descriptive statistics. These types of statistics summarize numerical information. For example, a teacher who calculates the mean, median, range, and standard deviation of a set of exam scores is using descriptive statistics. Descriptive statistics is the subject of the first part of this book.
The following are examples of the use (or misuse) of descriptive statistics.
Example 1.6 Baseball Players’ Batting Averages. Descriptive statistics can be used to provide a point of reference. The batting averages of baseball players are commonly reported in the newspapers, but to people unfamiliar with baseball, these numbers may be misleading. For example, Wade Boggs of the Boston Red Sox hit $.366$ in 1988; that is, he got a hit in almost $37 \%$ of his official at bats. Because he was unsuccessful over $63 \%$ of the time, however, a person with little knowledge of baseball might conclude that Boggs is an inferior hitter. Comparing Boggs’s average to the mean batting average of all players in the same year, which was $.285$, reveals that Boggs is among the best hitters.

Example 1. 7 Monthly Unemployment Rates. Graphical statistical analysis can be used to summarize small amounts of information. Figure $1.1$ displays the US unemployment rates for each month from January 2001 to July 2011. It shows, for instance, that the unemployment rates for December 2001, December 2005, and December 2010 were $5.7 \%, 4.9 \%$, and $9.4 \%$, respectively.

## 有限元方法代写

tatistics-lab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。

## 金融代写|利率理论代写portfolio theory代考|CORPFIN3501

statistics-lab™ 为您的留学生涯保驾护航 在代写利率理论portfolio theory方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写利率理论portfolio theory代写方面经验极为丰富，各种代写利率理论portfolio theory相关的作业也就用不着说。

• 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|利率理论代写portfolio theory代考|SPECTRUM OF PORTFOLIO MANAGERS

Financial advisors provide individual and institutional clients with asset allocation recommendations, manager search capabilities, manager monitoring, and performance and risk analysis. Registered investment advisors (RIA) cater to highnet-worth investors and may also provide tax guidance, insurance strategy, estate planning, and expense management services. In some cases, sophisticated RIAs may be defined as money therapists, helping clients process their feelings about wealth, charitable giving, and handling money within their family. High-end advisors typically charge basis point fees that decline with increasing asset levels. Family offices may provide services beyond strict money management, even providing travel agent functions.

Pension consultants recommend investments and managers for institutional investors. They tend to be more rigorous in their process than managers of high-networth assets-for example, studying liability dynamics when proposing asset allocation and funding policies for a DB plan. Although RIAs may have earned their Certified Financial Planner ${ }^{\circledR}$ designation, which includes topics in estate planning and tax policy, many pension consultants will have earned their Chartered Financial Analyst ${ }^{\text {A }}$ charter, a more rigorous professional certification. Many pension consulting firms have one or more liability actuaries on staff as well. Pension consultants talk in terms of benchmarks and portfolio risk, whereas advisors to smaller individual investors may focus on total assets. Although they are sophisticated, there is still a need to manage relations with pension clients. They may need to be educated about asset liability management, introduced to new asset classes, or supported in periods of unhealthy funding status. Pension plans, foundations, and endowments are known to blame (that is replace) their investment consultants when overall results are subpar.

## 金融代写|利率理论代写portfolio theory代考|LAYOUT OF THIS BOOK

Portfolio managers are charged with setting the weights of asset classes and individual securities. They need tools that will help them balance the returns and risks of investing in these assets through time. In many cases, risk and return are measured relative to a benchmark; in others, absolute return is the objective. Some portfolio managers prefer to make decisions based on fundamental information while others prefer utilizing mathematical models. In the following chapters, this book provides the basic tools for helping set investment weights for each of these scenarios. Several chapters use some mathematics to introduce the models; this approach is intended to help the reader develop the intuition needed to make effective decisions on asset and security selection. It also supports the development of the Excel-based tools designed to provide immediate, hands-on experience in applying key concepts.

Chapters 3-5 introduce and develop the tools for setting efficient asset allocations; Chapter 12 explains how to rebalance these weights through time. The techniques for setting weights of individual securities within asset classes are presented for equity and fixed income portfolios in Chapters 7-10. A discussion of alternative asset classes is the focus of Chapter 11 . Chapter 6 reviews the key ingredients for any successful active or passive investment strategy involving asset allocation or security selection.

Portfolio managers must be aware of important incentives and responsibilities to meet their clients’ needs. This book explains how the investment business works, including a review of business incentives that may motivate healthy or inappropriate behavior. This is the focus of Chapter 14 .

The investment business would not exist without clients. Clients have money they want to grow. They have liquidity needs. They are willing to pay a fee to portfolio managers if the managers can help them meet these goals, but they will not hesitate to terminate a relationship if the manager fails to deliver.

## 有限元方法代写

tatistics-lab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。