Posted on Categories:Financial Risk Management, 金融代写, 金融风险管理

# 金融代写|金融风险管理代写Financial Risk Management代考|CHEE6420 Credit derivatives

avatest™

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

•最快12小时交付

•200+ 英语母语导师

•70分以下全额退款

## 金融代写|金融风险管理代写Financial Risk Management代考|Credit derivatives

Definition
A credit default swap (CDS)is a contract in which the buyer makes a regular cash payment and the seller repays the face value of a bond if the underlying company defaults
Financial Risk Management (Lecture 6)
Credit derivatives
Andreas Krause $5 / 27$
Credit Default Swaps
Valuation of CDS

Assume defaults can only happen once a year in mid-year

Payments are due at the end of year and if the default happens in that year pro-rata for this year

The pricing determines the annual payments, the spread

Payments without default

Default intensity $\lambda$

Present value of payments for a $T$-year CDS

$P V_{\text {pay }}=s \sum_{t=1}^T(1-\lambda)^t e^{-r t}$
Payment with default

Default happens in mid-year, hence half the spread is payable

$P V_{\text {accrual }}=\frac{1}{2} s \sum_{t=1}^T \lambda(1-\lambda)^{t-1} e^{-r\left(t-\frac{1}{2}\right)}$

Payment with default

Default happens in mid-year, hence half the spread is payable

$P V_{\text {accrual }}=\frac{1}{2} s \sum_{t=1}^T \lambda(1-\lambda)^{t-1} e^{-r\left(t-\frac{1}{2}\right)}$
Financial Risk Management (Lecture 6)
Total payments

The total payments made by the buyer are

$P V_{\text {payments }}=s \sum_{t=1}^T(1-\lambda)^t e^{-r t}+\frac{1}{2} s \sum_{t=1}^T \lambda(1-\lambda)^{t-1} e^{-r\left(t-\frac{1}{2}\right)}$

$=s \sum_{t=1}^T(1-\lambda)^t e^{-r t}+\frac{1}{2} \frac{\lambda s}{1-\lambda} \sum_{t=1}^T(1-\lambda)^t e^{-r\left(t-\frac{1}{2}\right)}$

$=s\left(1+\frac{1}{2} \frac{\lambda}{1-\lambda} e^{\frac{1}{2} r}\right) \sum_{t=1}^T(1-\lambda)^t e^{-r t}$

## 金融代写|金融风险管理代写Financial Risk Management代考|Collaterized debt obilgations

Relevance of CDOs

CDOs have become the most widely used credit derivative

Large amounts of CDOs have been issued by banks are held within the financial sector

Losses from CDOs, especially also from higher tranches, have contributed to the credit crunch

The valuation of CDOs is very similar to a basket CDS

We need to find the probability of a loss for a given tranche and its distribution within a tranche

This can be achieved similarly to the probability of default in a basket CDS

The valuation is time-consuming but in principle not difficult

The problem

When trading derivatives the counterparty often has obligations:

Deliver the underlying asset

Make regular payments on the contract
Financial Risk Management (Lecture 6)
Collateral

Collateral reduces the counterparty exposure

Mark-to-market is commonly used

Often not sufficient for full coverage of the risks

## 金融代写|金融风险管理代写Financial Risk Management代考|Credit derivatives 定义 衍生 品Andreas

Krause5 $/ 27$
$\operatorname{CDS}$ 的信用违约互换估值

$$P V_{\text {pay }}=s \sum_{t=1}^T(1-\lambda)^t e^{-r t}$$

$$P V_{\text {accrual }}=\frac{1}{2} s \sum_{t=1}^T \lambda(1-\lambda)^{t-1} e^{-r\left(t-\frac{1}{2}\right)}$$

$$P V_{\text {accrual }}=\frac{1}{2} s \sum_{t=1}^T \lambda(1-\lambda)^{t-1} e^{-r\left(t-\frac{1}{2}\right)}$$

\begin{aligned} & P V_{\text {payments }}=s \sum_{t=1}^T(1-\lambda)^t e^{-r t}+\frac{1}{2} s \sum_{t=1}^T \lambda(1-\lambda)^{t-1} e^{-r\left(t-\frac{1}{2}\right)} \ & =s \sum_{t=1}^T(1-\lambda)^t e^{-r t}+\frac{1}{2} \frac{\lambda s}{1-\lambda} \sum_{t=1}^T(1-\lambda)^t e^{-r\left(t-\frac{1}{2}\right)} \ & =s\left(1+\frac{1}{2} \frac{\lambda}{1-\lambda} e^{\frac{1}{2} r}\right) \sum_{t=1}^T(1-\lambda)^t e^{-r t} \end{aligned}

## 金融代写|金融风险管理代写Financial Risk Management代考|Collaterized debt obilgations

CDO 的相关性

CDOs已成为最广泛使用的信用衍生品

CDO 的损失，尤其是较高档次的损失，导致了信贷紧缩

CDO 的估值与一篮子 CDS 非常相似

## 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。