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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|Overnight indexed swaps

The coupons of OISs differ from those of Ibor swaps. The coupons on an OIS are computed by compounding the overnight rates and are paid at the end of a given period (often three months or one year). Moreover, the payment is done with a lag (usually two days after the last fixing publication in EUR and USD). More details on the OIS conventions can be found in Appendix B.9.

In this scction we analyse the impact of the compounding on the pricing. The impact of compounding in the multi-curve framework was originally analysed in Quantitative Research (2012d).

The impact of the delayed payment is ignored here. It was proved in Henrard (2004) that the adjustment is minimal and can be neglected in practice. We will come back to the feature and propose its analysis in Chapter 6.

The description of an overnight indexed coupon is as follows. The times associated are denoted $t_i(i=0, \ldots, n)$. They correspond to successive business days in the relevant calendar. The fixing for the period $\left[t_{i-1}, t_i\right]$ is denoted $I_X^O\left(t_{i-1}\right)$ $(i=1, \ldots, n)$ and the accrual factor in the index convention is $\delta_i$.
The overnight indexed coupon pays the amount
$$\left(\prod_{i=1}^n\left(1+\delta_i I_X^O\left(t_{i-1}\right)\right)\right)-1$$
in $t_p$. In this section we suppose that $t_p=t_n$.
Let $P_X^O(s, t)$ denote the OIS forward curve in the multi-curve framework. The meaning of OIS forward curve is the one described in $\mathrm{I}^{\mathrm{CPN}}$ and its related definition: the pricing of a one period (from $t_s$ to $t_e$, paying $\delta_e I_e^O$ ) overnight index coupon is given in $s$ by
$$P_X^D\left(s, t_e\right) \delta F_X^O\left(s, t_s, t_e\right) .$$
As before we define
$$\beta_X^O(s, t, t+1 d)=\left(1+\delta F_X^O(s, t, t+1 d)\right) \frac{P_X^D(s, t+1 d)}{P_X^D(s, t)}$$
where $t+1 d$ has to be understood as $t$ plus one business day.

## 金融代写|金融模型代写Modelling in finance代考|Forex and cross-currency swaps

Up to now, everything discussed is valid for any currency and we have reviewed only single-currency instruments. We have also supposed that the risk-free curves are given.

For cross-currency instruments like forex swaps and cross-currency swaps, cashflows in different currencies are involved. Our convention is that the present value of each cash-flow is evaluated in its own currency; at this stage no conversion into another currency is done.

Forex spot, forward or swap are simply sets of fixed cash-flows in each currency. The cash-flows in one currency are valued using the relevant discounting curve and produce a result in that currency. The total present value is two amounts in two different currencies.

As described in Appendix B.14, the forex swaps are mainly interest rate products. The main market information they convey is the difference in interest rate for a given period between two currencies. As such, they create links between the curves in different currencies.
Through multi-currency instruments a link between the discounting curves in different currencies is imposed by the market. To keep the coherence of the framework, the curve in one currency follows from the choice in any other currency. The valuation of cross-currency swaps is done as for single-currency swaps. The present value of each coupon is computed (in its own currency) using the previous formulas, and they are added. The total present value is two amounts, one in each of the swap currencies. To convert the multi-currency amount to one currency, today’s exchange rate is used.

The existence of par forex and cross-currency swaps, that is, with zero total present value, will impose a relationship between discounting curves in different currencies and exchange rates. Note that it is the total converted present value which is null, not each of the present values in each currency. Each leg of a forex swap transaction does not have a zero present value. Even if the forex swaps are mainly interest rate products, and this is why they are used in curve calibration, they create small currency exposures. The currency exposure exists from the trading moment and does not only appear due to market movements. The only case where there is no currency exposure is when the interest rate in the first currency of the swap is zero over the swap period.

# 金融模型代写

## 金融代写|金融模型代写modeling in finance代考|隔夜指数互换

.

OISs的息票不同于Ibor掉期的息票。OIS的息票是由隔夜利率复合计算的，并在给定的期限(通常是三个月或一年)结束时支付。此外，支付有一个延迟(通常是在最后一次公布欧元和美元的定盘后两天)。关于OIS约定的更多细节可在附录B.9中找到

## 金融代写|金融模型代写modeling in finance代考|Forex and cross-currency swaps

. . modeling in finance “>金融代写|金融模型代写

## 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。

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