## 数学代写|金融衍生品代写Financial derivatives代考|FINE448

2022年10月6日

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## 数学代写|金融衍生品代写Financial derivatives代考|Overnight Indexed Swap

An overnight indexed swap (OIS) is an interest rate swap where the cash-flow of the floating leg is based on a floating rate calculated from the overnight rates such as Eonia or effective fed funds rate for the concerned period.

Consider the example of Eonia which is quoted on ACT/360. The floating rate for OIS of the $k$-th period $\left(t_{k-1}, t_k\right)$ will be calculated as the geometric average of Eon̄ī̄ fixin̄̄s::

$$R_k=\left[\prod_{i=1}^{N_{f i x}^k}\left(1+\frac{r_i \times n_i}{360}\right)-1\right] \frac{360}{N_k}$$
where
$R_k$ : rate for OIS of the $k$-th period
$N_{f i x}^k$ : total number of fixings of the overnight rate for the $k$-th period
$r_i$ : Eonia fixing rate for day $i$
$n_i:$ number of calendar days covered by $r_i$
$N_k$ : total number of calendar days for the $k$-th period
The rate of OIS implies less risk than the corresponding interbank lending rate such as Libor and Euribor because OIS rate is based on actual trades, which makes it more difficult to be manipulated.

Because of counterparty risk, the derivatives trades are normally collateralized. The cash collaterals are in general paid with overnight interest rate. As a consequence, it is considered as a secured lending rate, i.e. a proxy of risk-free rate. It is natural to apply OIS implied rates for discounting in financial calculation. Even though Libor and Euribor are widely used as reference for swaps, OIS is gaining increasing popularity. The OIS yield curve construction is similar to that for Libor rate based instruments.

## 数学代写|金融衍生品代写Financial derivatives代考|Other Swaps

There are other types of interest rate swap (called exotic swaps in general). Their valuation methods usually involve interest rate term structure modelling. The exotic swap valuation is often found to be the valuation of the comparable standard swap plus an extra term known as the convexity adjustment. We will mention only two of the most popular ones: constant maturity swap and in-arrears swap.

A constant maturity swap (CMS) is a swap in which the reference floating rate used for each settlement is the prevailing market rate of the standard swap of a specified fixed tenor. For example, in a 2 year maturity CMS swap linked to USD10Y swap rate, the cash flow for the floating leg is based on the market rate of the USD10Y swap rate observed at each settlement.

It is worth highlighting that the name $C M S$ rate in a structured product refers to the swap rate of specified tenor (e.g. USD20Y swap rate) to be observed on the scheduled date(s) of the product.

The in-arrears swap is a swap in which the floating rate is determined at the end of the period, instead of observing at the beginning for a standard swap.

A yield curve is a set of interest rate levels with equivalent credit quality across different tenors (also called pillars) in the same currency. ${ }^9$ The relationship between the interest rate levels of different tenors is called interest rate term structure.
The yield curve used in the financial market is also called zero coupon curve or simply zero curve because each point shows the market interest rate for a ZC bond (i.e. discount factor) of the related pillar. The zero coupon curve is built with the most liquid financial market instruments which are involved in the interest rate risk hedging. The interest rate level in any basis (e.g. continuous, money market, etc.) can be implied from the ZC bonds.

# 金融衍生品代写

## 数学代写|金融衍生品代写金融衍生品代考|隔夜指数掉期

$$R_k=\left[\prod_{i=1}^{N_{f i x}^k}\left(1+\frac{r_i \times n_i}{360}\right)-1\right] \frac{360}{N_k}$$
where
$R_k$ 的OIS的利率 $k$-th period
$N_{f i x}^k$ :隔夜拆借利率的定盘总数 $k$-th period
$r_i$ : Eonia日固定率 $i$
$n_i:$ 覆盖的日历天数 $r_i$
$N_k$ 的总日历天数 $k$OIS利率隐含的风险低于相应的银行间拆借利率，如Libor和Euribor，因为OIS利率是基于实际交易，这使得它更难以被操纵

## 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。