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# 金融代写|金融衍生品代写Financial Derivatives代考|Swap Contracts

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## 金融代写|金融衍生品代写Financial Derivatives代考|Swap Contracts

A swap contract is a contract in which two counterparties agree to make periodic payments that differ in a fundamental way from each other until some future date. The terms of a swap contract, besides the maturity and notional value of the contract, can include the currencies to be exchanged (foreign currency swap), the rate of interest applicable to each counterparty (interest rate swap), and the timetable by which payments are made. Swap contracts are an over-the-counter, negotiated derivative contract like a forward contract rather than an exchangetraded instrument like a futures contract. The swap contract counterparties must be classified as Eligible Contract Participants, as defined by the Commodity Exchange Act. $^3$ Although foreign currency swaps predate interest rate swaps, interest rate swaps are economically most important today.

Consider the uses for an interest rate swap. Suppose the swap contract specifies the exchange of floating rate cash flows for fixed rate cash flows. That is, a counterparty agrees to pay a fixed cash flow (based on a fixed rate) to another counterparty and in return receive a variable cash flow (based on a floating rate). The exchange of cash flows occurs periodically, say every six months; the cash flows are netted against each other so that whichever counterparty’s cash flow is larger, that counterparty pays the difference to the other. A swap of fixed rate for floating rate cash flows reduces the fixed rate payer’s exposure to unexpected rate increases, which is an important commercial risk for the holder of existing fixed-income securities or firms that anticipate the issuance of debt in the future. If rates rise during the contract’s life, the fixed rate payer will receive cash flows that offset the loss of value in existing securities or the increase in debt issuance cost. Similarly, the swap of floating rate for fixed rate cash flows reduces the floating-rate payer’s exposure to unexpected rate decreases.

Suppose in 1999, Maytag issues a three-year, \$100 million par floating rate note with semiannual interest payments at 80 basis points over the London Interbank Offered Rate (LIBOR), which is at 3.2 percent per annum. Maytag’s interest expense floats with LIBOR but at the current rate, Maytag will pay \$2.0 million as interest to the debt holders every six months, in March and September. Maytag is exposed to the commercial risk of unexpected increases in LIBOR. To transfer the risk, Maytag enters into a swap agreement with a U.S. commercial bank to pay a fixed 5 percent per annum on the $\$ 100$million until maturity. In return, the bank agrees to pay Maytag a variable amount based on LIBOR plus 80 basis points. Only the cash flow differential is exchanged in the agreement. Exhibit 1.10 is a table of the swap cash flows as LIBOR rises. Maytag makes increasing cash payments to debt holders as the rate floats higher; completely offsetting the interest expense are equivalent cash inflows from the U.S. commercial bank. Maytag still pays a fixed rate cash flow to the U.S. commercial bank of$\$2.5$ million every six months. Note that Maytag has credit risk exposure from the bank only when the value of the interest rate swap is positive (last column of Exhibit 1.10).

## 金融代写|金融衍生品代写Financial Derivatives代考|Option Contracts

Option contracts fall into one of two basic categories: calls or puts. In a call (put) option contract the contract buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the seller at a fixed price before a certain date. Every option contract has both a buyer and a seller. The contract buyer has a right but not an obligation to initiate an exchange; the seller is obligated to perform, however, should the buyer exercise the contract rights. The fixed price in an option contract is the exercise or strike price-the price at which the contract buyer either purchases from the contract seller (call option) or sells to the contract seller (put option). The contract maturity date is also called the contract expiration date. Finally, the option buyer makes a nonrefundable payment to the option seller, called the option premium, to obtain the rights of the option contract. The purpose of an option pricing model, such as the Black-Scholes model or the binomial model, is to estimate a “fair” option contract premium.

In general, a call option buyer (seller) expects the price of the underlying security to increase (decrease or stay steady) above the option exercise price. If not, the call option seller keeps the nonrefundable payment, the call option premium. A put option buyer (seller) expects the price of the underlying security to decrease (increase or stay steady) below the option exercise price. If so, the put option buyer can exercise the right to sell the underlying instrument to the put option seller at the relatively high exercise price. If an option contract is held to expiration, the option may expire worthless, be exercised by the contract buyer, or be sold for the difference between the contract exercise price and the market price of the underlying.

Consider the call option risk profile in Exhibit 1.12. The buyer of an option contract, call or put option, is called the option long; the option seller is called the option short. In Exhibit 1.12, if the unexpected change in the underlying instrument’s price, $\Delta P$, at option expiration is negative (or prices fall), the long call position is worthless and the call option buyer forfeits the call premium. At the same time, the short call option position is profitable by the amount of the premium. The horizontal, dashed lines to the left of the vertical axis illustrate the returns. If the unexpected change in the underlying instrument’s price, $\Delta P$, at option expiration is positive (or prices rise), the long call position increases the value of the option buyer, $\Delta V$. Before the option buyer can break even, however, the price must rise sufficiently to cover the nonrefundable option premium paid to the option short. At the same time, the short call position keeps part of the premium paid by the call long until prices rise sufficiently. The sloping, dashed lines to the right of the vertical axis illustrate the returns. Exhibit 1.12 shows that the risk profile of a long call position is similar to a long forward or long futures contract position. The risk profile of a short call option position is similar to a short forward or futures contract position but only if underlying prices rise.

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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。