# 金融代写|金融数学代写Financial Mathematics代考|TFIN101

## 金融代写|金融数学代写Financial Mathematics代考|Interest Rate Risk Management

Fixed-income portfolio management is usually focused on managing the interest rate risk of a portfolio relative to a benchmark or a related set of liabilities. Benchmarking is the process of identifying an index or other source of observable returns and using those returns as a point of reference for evaluating the success of an investment strategy. For example, a fixedincome manager for a mutual fund might desire that the effect of interest rate shifts on the manager’s portfolio be very close to the effects of the same interest rate shifts on the value of the manager’s benchmark such as a published index of bond returns. A fixed-income manager of a pension fund may be more concerned about making sure that the bond portfolio’s ability to provide funds to meet anticipated liabilities (pension benefits) is protected from interest rate shifts.

The process of ensuring that the goals for a fixed-income portfolio (benchmarking or liability funding) will be met despite interest rate changes is known as immunization. One of the premier methods of obtaining immunization is duration matching. In the case of a mutual fund manager attempting to track a benchmark such as a major bond index, the manager will tend to make sure that the duration of her portfolio is very close to the duration of the benchmark. In the case of a pension fund manager attempting to ensure that the fund’s investments will be able to meet the pension obligations that manager will tend to make sure that the duration of her portfolio is very close to the duration of the plan’s anticipated liabilities (assuming the plan is fully funded with the value of the investments equaling the present value of the liabilities).

Another method of interest rate risk management is cash flow matching (i.e., matching the various cash flow longevities of the portfolio to the cash flow longevities of the benchmark or liability stream). The problem with cash flow matching is that it can be very inflexible with regard to the investment opportunities that the manager can select.
Duration provides a first-order solution that permits flexibility. The inclusion of convexity matching tends to improve the accuracy of the immunization but also tends to restrict the flexibility of the manager to include diverse investment opportunities.
In Chapter 5, we will discuss hedging strategies to manage interest rate risk using duration in detail. In the next subsection, we will discuss other risks associated with fixed-income security: credit risk and default risk. The management of credit risk and default risk will be discussed in detail in Chapter 8 .

## 金融代写|金融数学代写Financial Mathematics代考|Introduction to Credit Risk and Default Risk

Credit risk refers to uncertainty regarding a borrower’s ability to make timely interest and principal payments. Credit risk includes: (1) volatility of market prices caused by changes in a borrower’s perceived ability to meet debt obligations, (2) fluctuations in the risk premiums (credit spreads) throughout the credit markets, and (3) losses due to defaults. Default risk is the risk that the borrower will make only partial payments, no payments, and/or delayed payments.
In the case of fixed income assets that have no risk of default, the present value or market value of the asset can be found by discounting the promised cash flows at the riskless interest rates corresponding to the longevity of each cash flow. In the case of fixed-income investments (not derivatives) with default risk, the present value or market value of the asset is found by discounting the promised cash flows with a risky discount rate that is equal to the sum of a riskless interest rate and a credit spread, s. Equation $2.22$ modifies the general asset valuation formula (Equation 2.10) by including a discount factor that captures the effect of potential default through the inclusion of a credit spread
$$\tilde{B}(0, T)=\sum_{i=1}^n C_{t_i} e^{-\left(r_i+s\right) t_i}$$
where $\tilde{B}(0, T)$ is the $T$ year risky bond price today.
Equation $2.22$ is based on a term-structure approach in which cash flows of different longevity are discounted at interest rates corresponding to the cash flow’s longevity. Equation $2.23$ illustrates the use of a credit spread in a yield-based valuation model in which all cash flows are discounted at the same rate $(y)$ in which $y$ contains the credit spread
$$\tilde{B}(0, T)=\sum_{i=1}^n C_{t_i} e^{-y t_i}$$
where $y$ is the risky bond yield.
If the term structure of risk-free interest rates is flat, then Equation $2.22$ becomes:
$$\tilde{B}(0, T)=\sum_{i=1}^n C_{t_i} e^{-(r+s) t_i}$$
Comparing Equations (2.23) and (2.24), note that we use $y=r+s$ in Equation $2.24$ in which $s$ is the yield spread or credit spread.

## 金融代写|金融数学代写金融数学代考|利率风险管理

Duration提供了一阶解决方案，允许灵活性。包含凸度匹配往往会提高免疫的准确性，但也往往会限制经理人包含不同投资机会的灵活性。在第五章中，我们将详细讨论利用期限管理利率风险的套期保值策略。在下一小节中，我们将讨论与固定收益证券相关的其他风险:信用风险和违约风险。第8章将详细讨论信用风险和违约风险的管理

## 金融代写|金融数学代写金融数学代考|信用风险与违约风险简介

.

$$\tilde{B}(0, T)=\sum_{i=1}^n C_{t_i} e^{-\left(r_i+s\right) t_i}$$
，其中$\tilde{B}(0, T)$是当前$T$年风险债券价格，从而包含了一个捕捉潜在违约影响的贴现因子。公式$2.22$基于期限结构方法，其中不同寿命的现金流按现金流寿命对应的利率折现。公式$2.23$说明了在基于收益的估值模型中使用信用利差，其中所有现金流以相同的比率贴现$(y)$，其中$y$包含信用利差
$$\tilde{B}(0, T)=\sum_{i=1}^n C_{t_i} e^{-y t_i}$$
，其中$y$是风险债券收益率。如果无风险利率期限结构是平坦的，则公式$2.22$变成:
$$\tilde{B}(0, T)=\sum_{i=1}^n C_{t_i} e^{-(r+s) t_i}$$

myassignments-help数学代考价格说明

1、客户需提供物理代考的网址，相关账户，以及课程名称，Textbook等相关资料~客服会根据作业数量和持续时间给您定价~使收费透明，让您清楚的知道您的钱花在什么地方。

2、数学代写一般每篇报价约为600—1000rmb，费用根据持续时间、周作业量、成绩要求有所浮动(持续时间越长约便宜、周作业量越多约贵、成绩要求越高越贵)，报价后价格觉得合适，可以先付一周的款，我们帮你试做，满意后再继续，遇到Fail全额退款。

3、myassignments-help公司所有MATH作业代写服务支持付半款，全款，周付款，周付款一方面方便大家查阅自己的分数，一方面也方便大家资金周转，注意:每周固定周一时先预付下周的定金，不付定金不予继续做。物理代写一次性付清打9.5折。

Math作业代写、数学代写常见问题

myassignments-help擅长领域包含但不是全部: