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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|金融模型代写Modelling in finance代考|Interest rate swap

With hypothesis $\mathrm{I}^{\mathrm{CPN}}$ and the related definition, the computation of the present value of vanilla IRSs is straightforward. The definition was selected for that reason. An IRS is described by a set of fixed coupons or cash-flows $c_i$ at dates $\tilde{t}i(1 \leq i \leq \tilde{n})$. For those flows, the discounting curve is used. It also contains a set of floating coupons over the periods $\left[t{i-1}, t_i\right]$ with $t_i=t_{i-1}+j(1 \leq i \leq n)$. The accrual factors for the periods $\left[t_{i-1}, t_i\right]$ are denoted $\delta_i$. The value of a (fixed rate) receiver IRS in $t<t_0$ is
$$\sum_{i=1}^{\tilde{n}} c_i P_X^D\left(t, \tilde{t}i\right)-\sum{i=1}^n P_X^D\left(t, t_i\right) \delta_i F_X^{\mathrm{CPN}, j}\left(t, t_{i-1}, t_i\right) .$$
In the textbook one-curve pricing approach, the IRSs are usually priced through either the discounting forward rate approach or the cash-flow equivalent approach. The discounting forward rate approach is similar to the above formula.

The cash-flow equivalent approach consists in replacing, for valuation purposes, the (receiving) floating leg by receiving the notional at the period start and paying the notional at the period end. We would like to have a similar result in our new framework. To this end we have the following definition.

Definition $2.3$ (Multiplicative coupon spread). The multiplicative spread between a forward curve and the discounting curve is
$$\beta_X^{\mathrm{CPN}, j}(t, u, v)=\left(1+\delta F_X^{\mathrm{CPN}, j}(t, u, v)\right) \frac{P_X^D(t, v)}{P_X^D(t, u)}=\frac{1+\delta F_X^{\mathrm{CPN}, j}(t, u, v)}{1+\delta F_X^D(t, u, v)} .$$
This type of multiplicative spread is quite natural in the interest rate context. The factor $\beta$ is the investment factor to be composed with the risk-free investment factor to obtain the Ibor investment factor. It could also be written as
$$\left(1+\delta F_X^D(t, u, v)\right)\left(1+\delta F_X^\beta\right)=\left(1+\delta F_X^{\mathrm{CPN}, j}(t, u, v)\right)$$
for a clear definition of $F_X^\beta$.

## 金融代写|金融模型代写Modelling in finance代考|In practice: swap fixing

The description of swaps above is valid for swaps with one fixed leg and the other leg made of floating coupons only. In practice, this is not the case for most of the swaps on the trade date. The standard swaps are traded with an effective date equal to the spot date. The definition of spot is different for each currency and is described in Section B.8.

When the Ibor index fixing for the day has already taken place (after 11:00 am London time for Libor), the first coupon of the floating leg is not a floating coupon anymore but a fixed coupon. In that case, the value of the swap is
$$\sum_{i=1}^{\tilde{n}} c_i P_X^D\left(t, \tilde{t}i\right)-P_X^D\left(t, t_1\right) \delta_1 I_X^j\left(t^\right)-\sum{i=2}^n P_X^D\left(t, t_i\right) \delta_i F_X^{\mathrm{CPN}, j}\left(t, t_{i-1}, t_i\right)$$
where $t^$ is the fixing time. In practice, it is important in the valuation, including when calibrating the curves, to clearly distinguish between the coupons that have already been fixed and the ones that have not.

More generally the swaps that have aged or seasoned, that is, swap after their trading date, will also have one or more of the floating coupons already fixed. Most of the time, one of the coupons is fixed. If the valuation time is between the fixing of one coupon, except the first one, and the payment date of the previous one, there will be two fixed coupons.

# 金融模型代写

## 金融代写|金融模型代写modeling in finance代考|利率互换

.

$$\sum_{i=1}^{\tilde{n}} c_i P_X^D\left(t, \tilde{t}i\right)-\sum{i=1}^n P_X^D\left(t, t_i\right) \delta_i F_X^{\mathrm{CPN}, j}\left(t, t_{i-1}, t_i\right) .$$

$$\beta_X^{\mathrm{CPN}, j}(t, u, v)=\left(1+\delta F_X^{\mathrm{CPN}, j}(t, u, v)\right) \frac{P_X^D(t, v)}{P_X^D(t, u)}=\frac{1+\delta F_X^{\mathrm{CPN}, j}(t, u, v)}{1+\delta F_X^D(t, u, v)} .$$

$$\left(1+\delta F_X^D(t, u, v)\right)\left(1+\delta F_X^\beta\right)=\left(1+\delta F_X^{\mathrm{CPN}, j}(t, u, v)\right)$$
，以明确定义$F_X^\beta$ .

## 金融代写|金融模型代写modeling in finance代考| in practice: swap fixing

.

$$\sum_{i=1}^{\tilde{n}} c_i P_X^D\left(t, \tilde{t}i\right)-P_X^D\left(t, t_1\right) \delta_1 I_X^j\left(t^\right)-\sum{i=2}^n P_X^D\left(t, t_i\right) \delta_i F_X^{\mathrm{CPN}, j}\left(t, t_{i-1}, t_i\right)$$
，其中$t^$是固定时间。在实际操作中，在估值中，包括在校准曲线时，清楚地区分已经固定的息票和尚未固定的息票是很重要的 更一般地说，已经老化或经验丰富的掉期，即在交易日后的掉期，也会有一个或多个浮动息票已经固定。大多数时候，一种优惠券是固定的。如果估值时间介于固定一张息票(除第一张息票外)和前一张息票的付款日之间，则会有两张固定息票。

## 有限元方法代写

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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。

assignmentutor™您的专属作业导师
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