CHAPTER 13
INTEREST RATE DERIVATIVE INSTRUMENTS
I. INTRODUCTION
In this chapter we turn our attention to financial contracts that are popularly referred to as interest rate derivative instruments because they derive their value from some cash market instrument or reference interest rate. These instruments include futures, forwards, options, swaps, caps, and floors. In this chapter we will discuss the basic features of these instruments and in the next we will see how they are valued.
Why would a portfolio manager be motivated to use interest rate derivatives rather than the corresponding cash market instruments. There are three principal reasons for doing this when there is a well-developed interest rate derivatives market for a particular cash market instrument. First, typically it costs less to execute a transaction or a strategy in the interest rate derivatives market in order to alter the interest rate risk exposure of a portfolio than to make the adjustment in the corresponding cash market. Second, portfolio adjustments typically can be accomplished faster in the interest rate derivatives market than in the corresponding cash market. Finally, interest rate derivative may be able to absorb a greater dollar transaction amount without an adverse effect on the price of the derivative instrument compared to the price effect on the cash market instrument; that is, the interest rate derivative may be more liquid than the cash market. To summarize: There are three potential advantages that motivate the use of interest rate derivatives: cost, speed, and liquidity.
II . INTEREST RATE FUTURES
A futures contract is an agreement that requires a party to the agreement either to buy or sell something at a designated future date at a predetermined price. Futures contracts are products created by exchanges. Futures contracts based on a financial instrument or a financial index are known as financial futures. Financial futures can be classified as (1) stock index futures, (2) interest rate futures, and (3) currency futures. Our focus in this chapter is on interest rate futures.
A. Mechanics of Futures Trading
A futures contract is an agreement between a buyer (seller) and an established exchange or its clearinghouse in which the buyer (seller) agrees to take (make) delivery of something (the underlying) at a specified price at the end of a designated period of time. The price at which the parties agree to transact in the future is called the futures price. The designated date at which the parties must transact is called the settlement date or delivery date.
1. Liquidating a Position Most financial futures contracts have settlement dates in the months of March, June, September, and December. This means that at a predetermined time in the contract settlement month the contract stops trading, and a price is determined by the exchange for settlement of the contract. The contract with the closest settlement date is called the nearby futures contract. The next futures contract is the one that settles just after the nearby futures contract. The contract farthest away in time from settlement is called the most distant futures contract.
A party to a futures contract has two choices on liquidation of the position. First, the position can be liquidated prior to the settlement date. For this purpose, the party must take an offsetting position in the same contract. For the buyer of a futures contract, this means selling the same number of the identical futures contracts; for the seller of a futures contract, this means buying the same number of identical futures contracts.
The alternative is to wait until the settlement date. At that time the party purchasing a futures contract accepts delivery of the underlying at the agreed-upon price; the party that sells a futures contract liquidates the position by delivering the underlying at the agreed-upon price. For some interest rate futures contracts, settlement is made in cash only. Such contracts are referred to as cash settlement contracts.
2. The Role of the Clearinghouse Associated with every futures exchange is a clearinghouse, which performs several functions. One of these functions is to guarantee that the two parties to the transaction will perform.
When an investor takes a position in the futures market, the clearinghouse takes the opposite position and agrees to satisfy the terms set forth in the contract. Because of the clearinghouse, the investor need not worry about the financial strength and integrity of the party taking the opposite side of the contract. After initial execution of an order, the relationship between the two parties ends. The clearinghouse interposes itself as the buyer for every sale and the seller for every purchase. Thus investors are free to liquidate their positions without involving the other party in the original contract, and without worrying that the other party may default. This is the reason that we define a futures contract as an agreement between a party and a clearinghouse associated with an exchange. Besides its guarantee function, the clearinghouse makes it simple for parties to a futures contract to unwind their positions prior to the settlement date.
3. Margin Requirements When a position is first taken in a futures contract, the investor must deposit a minimum dollar amount per contract as specified by the exchange. This amount is called initial margin and is required as deposit for the contract. The initial margin may be in the form of an interest-bearing security such as a Treasury bill. As the price of the futures contract fluctuates, the value of the margin account changes. Marking to market means effectively replacing the initiation price with a current settlement price. The contract thus has a new settlement price. At the end of each trading day, the exchange determines the current settlement price for the futures contract. This price is used to mark to market the investor’s position, so that any gain or loss from the position is reflected in the margin account.172
Maintenance margin is the minimum level (specified by the exchange) to which the margin account may fall to as a result of an unfavorable price movement before the investor is required to deposit additional margin. The additional margin deposited is called variation margin, and it is an amount necessary to bring the account back to its initial margin level. This amount is determined from the process of marking the position to market. Unlike initial margin, variation margin must be in cash, not interest-bearing instruments. Any excess margin in the account may be withdrawn by the investor. If a party to a futures contract who is required to deposit variation margin fails to do so within 24 hours, the futures position is closed out.
Although there are initial and maintenance margin requirements for buying securities on margin, the concept of margin differs for securities and futures. When securities are acquired on margin, the difference between the price of the security and the initial margin is borrowed from the broker. The security purchased serves as collateral for the loan, and the investor pays interest. For futures contracts, the initial margin, in effect, serves as “good faith” money, an indication that the investor will satisfy the obligation of the contract.
B. Forward Contracts
A forward contract, just like a futures contract, is an agreement for the future delivery of something at a specified price at the end of a designated period of time. Futures contracts are standardized agreements as to the delivery date (or month) and quality of the deliverable, and are traded on organized exchanges. A forward contract differs in that it is usually non-standardized (that is, the terms of each contract are negotiated individually between buyer and seller), there is no clearinghouse, and secondary markets are often non-existent or extremely thin. Unlike a futures contract, which is an exchange-traded product, a forward contract is an over-the-counter instrument.
Futures contracts are marked to market at the end of each trading day. Consequently, futures contracts are subject to interim cash flows as additional margin may be required in the case of adverse price movements, or as cash is withdrawn in the case of favorable price movements. A forward contract may or may not be marked to market, depending on the wishes of the two parties. For a forward contract that is not marked to market, there are no interim cash flow effects because no additional margin is required.
Finally, the parties in a forward contract are exposed to credit risk because either party may default on its obligation. This risk is called counterparty risk. This risk is minimal in the case of futures contracts because the clearinghouse associated with the exchange guarantees the other side of the transaction. In the case of a forward contract, both parties face counterparty risk. Thus, there exists bilateral counterparty risk.
Other than these differences, most of what we say about futures contracts applies equally to forward contracts.
C. Risk and Return Characteristics of Futures Contracts
When an investor takes a position in the market by buying a futures contract, the investor is said to be in along position or to belong futures. The buyer of the futures contract is also referred to as the “long.” If, instead, the investor’s opening position is the sale of a futures contract, the investor is said to be in a short position or to be short futures. The seller of the futures contract is also referred to as the “short.” The buyer of a futures contract will realize a profit if the futures price increases; the seller of a futures contract will realize a profit if the futures price decreases.
When a position is taken in a futures contract, the party need not put up the entire amount of the investment. Instead, only initial margin must be put up. Consequently, an investor can effectively create a leveraged position by using futures. At first, the leverage available in the futures market may suggest that the market benefits only those who want to speculate on price movements. This is not true. As we shall see, futures markets can be used to control interest rate risk. Without the effective leverage possible in futures transactions, the cost of reducing price risk using futures would be too high for many market participants.
D. Exchange-Traded Interest Rate Futures Contracts
Interest rate futures contracts can be classified by the maturity of their underlying security. Short-term interest rate futures contracts have an underlying security that matures in less than one year. Examples of these are futures contracts in which the underlying is a 3-month Treasury bill and a 3-month Eurodollar certificate of deposit. The maturity of the underlying security of long-term futures contracts exceeds one year. Examples of these are futures contracts in which the underlying is a Treasury coupon security, a 10-year agency note, and a municipal bond index. Our focus will be on futures contracts in which the underlying is a Treasury coupon security (a Treasury bond or a Treasury note). These contracts are the most widely used by managers of bond portfolios and we begin with the specifications of the Treasury bond futures contract. We will also discuss the agency note futures contracts.
There are futures contracts on non-U.S. government securities traded throughout the world. Many of them are modeled after the U.S. Treasury futures contracts and consequently, the concepts discussed below apply directly to those futures contracts.
1. Treasury Bond Futures The Treasury bond futures contract is traded on the Chicago Board of Trade (CBOT). The underlying instrument for a Treasury bond futures contract is $100,000 par value of a hypothetical 20-year coupon bond. The coupon rate on the hypothetical bond is called the notional coupon.
The futures price is quoted in terms of par being 100. Quotes are in 32nds of 1%. Thus a quote for a Treasury bond futures contract of 97-16 means 97 and 
or 97.50. So, if a buyer and seller agree on a futures price of 97-16, this means that the buyer agrees to accept delivery of the hypothetical underlying Treasury bond and pay 97.50% of par value and the seller agrees to accept 97.50% of par value. Since the par value is $100,000, the futures price that the buyer and seller agree to for this hypothetical Treasury bond is $97,500.
or 97.50. So, if a buyer and seller agree on a futures price of 97-16, this means that the buyer agrees to accept delivery of the hypothetical underlying Treasury bond and pay 97.50% of par value and the seller agrees to accept 97.50% of par value. Since the par value is $100,000, the futures price that the buyer and seller agree to for this hypothetical Treasury bond is $97,500.The minimum price fluctuation for the Treasury bond futures contract is 
of 1%, which is referred to as “a 32nd.” The dollar value of a 32nd for $100,000 par value (the par value for the underlying Treasury bond) is $31.25. Thus, the minimum price fluctuation is $31.25 for this contract.
of 1%, which is referred to as “a 32nd.” The dollar value of a 32nd for $100,000 par value (the par value for the underlying Treasury bond) is $31.25. Thus, the minimum price fluctuation is $31.25 for this contract.EXHIBIT: U.S Treasury Bond Issues Acceptable for Delivery and Conversion Factors
Eligible for Delivery of May 29.2002.
Source: Chicago Board or Trade
We have been referring to the underlying as a hypothetical Treasury bond. The seller of a Treasury bond futures contract who decides to make delivery rather than liquidate the position by buying back the contract prior to the settlement date must deliver some Treasury bond issue. But what Treasury bond issue? The CBOT allows the seller to deliver one of several Treasury bonds that the CBOT designates as acceptable for delivery. The specific issues that the seller may deliver are published by the CBOT for all contracts by settlement date. The CBOT makes its determination of the Treasury bond issues that are acceptable for delivery from all outstanding Treasury bond issues that have at least 15 years to maturity from the date of delivery.
Exhibit 1 shows the Treasury bond issues that the seller could have selected to deliver to the buyer of the CBOT Treasury bond futures contract as of May 29, 2002. Should the U.S. Department of the Treasury issue any Treasury bonds that meet the CBOT criteria for eligible delivery, those issues would be added to the list. Notice that for the Treasury bond futures contract settling (i.e., maturing) in March 2005, notice that there are 25 eligible issues. For contracts settling after March 2005, there are fewer than 25 eligible issues due to the shorter maturity of each previous eligible issue that results in a maturity of less than 15 years.
Although the underlying Treasury bond for this contract is a hypothetical issue and therefore cannot itself be delivered into the futures contract, the contract is not a cash settlement contract. The only way to close out a Treasury bond futures contract is to either initiate an offsetting futures position, or to deliver a Treasury bond issue satisfying the above-mentioned criteria into the futures contract.
a. Conversion Factors The delivery process for the Treasury bond futures contract makes the contract interesting. At the settlement date, the seller of a futures contract (the short) is now required to deliver to the buyer (the long) $100,000 par value of a 6% 20-year Treasury bond. Since no such bond exists, the seller must choose from one of the acceptable deliverable Treasury bonds that the CBOT has specified. Suppose the seller is entitled to deliver $100,000 of a 5% 20-year Treasury bond to settle the futures contract. The value of this bond is less than the value of a 6% 20-year bond. If the seller delivers the 5% 20-year bond, this would be unfair to the buyer of the futures contract who contracted to receive $100,000 of a 6% 20-year Treasury bond. Alternatively, suppose the seller delivers $100,000 of a 7% 20-year Treasury bond. The value of a 7% 20-year Treasury bond is greater than that of a 6% 20-year bond, so this would be a disadvantage to the seller.
How can this problem be resolved? To make delivery equitable to both parties, the CBOT has introduced conversion factors for adjusting the price of each Treasury issue that can be delivered to satisfy the Treasury bond futures contract. The conversion factor is determined by the CBOT before a contract with a specific settlement date begins trading.173 The adjusted price is found by multiplying the conversion factor by the futures price. The adjusted price is called the converted price.
Exhibit 1 shows conversion factors as of May 29, 2002. The conversion factors are shown by contract settlement date. Note that the conversion factor depends not only on the issue delivered but also on the settlement date of the contract. For example, look at the first issue in Exhibit 1, the 5¼% coupon bond maturing 11/15/28. For the Treasury bond futures contract settling (i.e., maturing) in March 2005, the conversion factor is 0.9062. For the December 2005 contract, the conversion factor is 0.9075.
The price that the buyer must pay the seller when a Treasury bond is delivered is called the invoice price. The invoice price is the futures settlement price plus accrued interest. However, as just noted, the seller can deliver one of several acceptable Treasury issues and to make delivery fair to both parties, the invoice price must be adjusted based on the actual Treasury issue delivered. It is the conversion factors that are used to adjust the invoice price. The invoice price is:
invoice price = contract size × futures settlement price × conversion factor
+ accrued interest
+ accrued interest
Suppose the Treasury March 2006 futures contract settles at 105-16 and that the issue delivered is the 8% of 11/15/21. The futures contract settlement price of 105-16 means 105.5% of par value or 1.055 times par value. As indicated in Exhibit 1, the conversion factor for this issue for the March 2006 contract is 1.2000. Since the contract size is $100,000, the invoice price the buyer pays the seller is:
$100, 000 × 1.055 × 1.2000 + accrued interest = $126, 600 + accrued interest
b. Cheapest-to-Deliver Issue As can be seen in Exhibit 1, there can be more than one issue that is permitted to be delivered to satisfy a futures contract. In fact, for the March 2005 contract, there are 25 deliverable or eligible bond issues. It is the short that has the option of selecting which one of the deliverable bond issues if he decides to deliver.174 The decision of which one of the bond issues a short will elect to deliver is not made arbitrarily. There is an economic analysis that a short will undertake in order to determine the best bond issue to deliver. In fact, as we will see, all of the elements that go into the economic analysis will be the same for all participants in the market who are either electing to deliver or who are anticipating delivery of one of the eligible bond issues. In this section, how the best bond issue to deliver is determined will be explained.
The economic analysis is not complicated. The basic principle is as follows. Suppose that an investor enters into the following two transactions simultaneously:
1. buys one of the deliverable bond issues today with borrowed money and
2. sells a futures contract
The two positions (i.e., the long position in the deliverable bond issue purchased and the short position in the futures contract) will be held to the delivery date. At the delivery date, the bond issue purchased will be used to satisfy the short’s obligation to deliver an eligible bond issue. The simultaneous transactions above and the delivery of the acceptable bond issue purchased to satisfy the short position in the futures contract is called a cash and carry trade. We will discuss this in more detail in the next chapter where the importance of selecting the best bond issue to deliver for the pricing of a futures contract is explained.
Let’s look at the economics of this cash and carry trade. The investor (who by virtue of the fact that he sold a futures contract is the short), has synthetically created a short-term investment vehicle. The reason is that the investor has purchased a bond issue (one of the
deliverable bond issues) and at the delivery date delivers that bond issue and receives the futures price. So, the investor knows the cost of buying the bond issue and knows how much will be received from the investment. The amount received is the coupon interest until the delivery date, any reinvestment income from reinvesting coupon payments, and the futures price at the delivery date. (Remember that the futures price at the delivery date for a given deliverable bond issue will be its converted price.) Thus, the investor can calculate the rate of return that will be earned on the investment. In the futures market, this rate of return is called the implied repo rate.An implied repo rate can be calculated for every deliverable bond issue. For example, suppose that there are N deliverable bond issues that can be delivered to satisfy a bond futures contract. Market participants who want to know either the best issue to deliver or what issue is likely to be delivered will calculate an implied repo rate for all N eligible bond issues. Which would be the best issue to deliver by a short? Since the implied repo rate is the rate of return on an investment, the best bond issue is the one that has the highest implied repo rate (i.e., the highest rate of return). The bond issue with the highest implied repo rate is called the cheapest-to-deliver issue.
Now that we understand the economic principle for determining the best bond issue to deliver (i.e., the cheapest-to-deliver issue), let’s look more closely at how one calculates the implied repo rate for each deliverable bond issue. This rate is computed using the following information for a given deliverable bond issue:
1. the price plus accrued interest at which the Treasury issue could be purchased
2. the converted price plus the accrued interest that will be received upon delivery of that Treasury bond issue to satisfy the short futures position
3. the coupon payments that will be received between today and the date the issue is delivered to satisfy the futures contract.
4. the reinvestment income that will be realized on the coupon payments between the time the interim coupon payment is received and the date that the issue is delivered to satisfy the Treasury bond futures contract.
The first three elements are known. The last element will depend on the reinvestment rate that can be earned. While the reinvestment rate is unknown, typically this is a small part of the rate of return and not much is lost by assuming that the implied repo rate can be predicted with certainty.
The general formula for the implied repo rate is as follows:
where days1 is equal to the number of days until settlement of the futures contract. Below we will explain the other components in the formula for the implied repo rate.
Let’s begin with the dollar return. The dollar return for an issue is the difference between the proceeds received and the cost of the investment. The proceeds received are equal to the proceeds received at the settlement date of the futures contract and any interim coupon payment plus interest from reinvesting the interim coupon payment. The proceeds received at the settlement date include the converted price (i.e., futures settlement price multiplied by the conversion factor for the issue) and the accrued interest received from delivery of the issue. That is,
proceeds received = converted price + accrued interest received + interim coupon payment
+ interest from reinvesting the interim coupon payment
As noted earlier, all of the elements are known except the interest from reinvesting the interim coupon payment. This amount is estimated by assuming that the coupon payment can be reinvested at the term repo rate. Later, we describe the repo market and the term repo rate. The term repo rate is not only a borrowing rate for an investor who wants to borrow in the repo market but also the rate at which an investor can invest proceeds on a short-term basis. For how long is the reinvestment of the interim coupon payment? It is the number of days from when the interim coupon payment is received and the actual delivery date to satisfy the futures contract. The reinvestment income is then computed as follows:
where
interest from reinvesting the interim coupon payment
= interim coupon × term repo rate × (days2/360)
= interim coupon × term repo rate × (days2/360)
days2 = number of days between when the interim coupon payment is received and the actual delivery date of the futures contract
The reason for dividing days2 by 360 is that the ratio represents the number of days the interim coupon is reinvested as a percentage of the number of days in a year as measured in the money market.
The cost of the investment is the amount paid to purchase the issue. This cost is equal to the purchase price plus accrued interest paid. That is,
cost of the investment = purchase price + accrued interest paid
Thus, the dollar return for the numerator of the formula for the implied repo rate is equal to
dollar return = proceeds received − cost of the investment
The dollar return is then divided by the cost of the investment.175
So, now we know how to compute the numerator and the denominator in the formula for the implied repo rate. The second ratio in the formula for the implied repo rate simply involves annualizing the return using a convention in the money market for the number of days. (Recall that in the money market the convention is to use a 360 day year.) Since the investment resulting from the cash and carry trade is a synthetic money market instrument, 360 days are used.
Let’s compute the implied repo rate for a hypothetical issue that may be delivered to satisfy a hypothetical Treasury bond futures contract. Assume the following for the deliverable issue and the futures contract:
Futures contract
futures price = 96
days to futures delivery date (days1) = 82 days
Deliverable issue
price of issue = 107
accrued interest paid = 3.8904
coupon rate = 10%
days remaining before interim coupon paid = 40 days
interim coupon = $5
number of days between when the interim coupon payment is received and the actual delivery date of the futures contract (days2) = 42
conversion factor = 1.1111
accrued interest received at futures settlement date = 1.1507
Other information:
42-day term repo rate = 3.8%
Let’s begin with the proceeds received. We need to compute the converted price and the interest from reinvesting the interim coupon payment. The converted price is:
The interest from reinvesting the interim coupon payment depends on the term repo rate.
The term repo rate is assumed to be 3.8%. Therefore,
To summarize:
| converted price | = | 106.6656 |
| accrued interest received at futures settlement date | = | 1.1507 |
| interim coupon payment | = | 5.0000 |
| interest from reinvesting the interim coupon payment | = | 0.0222 |
| proceeds received | = | 112.8385 |
The cost of the investment is the purchase price for the issue plus the accrued interest paid, as shown below:
cost of the investment = 107 + 3.8904 = 110.8904
EXHIBIT 2 Delivery Options Granted to the Short (Seller) of a CBOT Treasury Bond Futures Contract
| Delivery option | Description |
|---|---|
| Quality or swap option | Choice of which acceptable Treasury issue to deliver |
| Timing option | Choice of when in delivery month to deliver |
| Wild card option | Choice to deliver after the closing price of the futures contract is determined |
The implied repo rate is then:
Once the implied repo rate is calculated for each deliverable issue, the cheapest-to-deliver issue will be the one that has the highest implied repo rate (i.e., the issue that gives the maximum return in a cash-and-carry trade). As explained in the next chapter, this issue plays a key role in the pricing of a Treasury bond futures contract.
While an eligible bond issue may be the cheapest to deliver today, changes in factors may cause some other eligible bond issue to be the cheapest to deliver at a future date. A sensitivity analysis can be performed to determine how a change in yield affects the cheapest to deliver.
c. Other Delivery Options In addition to the choice of which acceptable Treasury issue to deliver—sometimes referred to as the quality option or swap option—the short has at least two more options granted under CBOT delivery guidelines. The short is permitted to decide when in the delivery month delivery actually will take place. This is called the timing option. The other option is the right of the short to give notice of intent to deliver up to 8:00 p.m. Chicago time after the closing of the exchange (3:15 p.m. Chicago time) on the date when the futures settlement price has been fixed. This option is referred to as the wild card option. The quality option, the timing option, and the wild card option (in sum referred to as the delivery options), mean that the long position can never be sure which Treasury bond will be delivered or when it will be delivered. These three delivery options are summarized in Exhibit 2.
d. Delivery Procedure For a short who wants to deliver, the delivery procedure involves three days. The first day is the position day. On this day, the short notifies the CBOT that it intends to deliver. The short has until 8:00 p.m. central standard time to do so. The second day is the notice day. On this day, the short specifies which particular issue will be delivered. The short has until 2:00 p.m. central standard time to make this declaration. (On the last possible notice day in the delivery month, the short has until 3:00 p.m.) The CBOT then selects the long to whom delivery will be made. This is the long position that has been outstanding for the greatest period of time. The long is then notified by 4:00 p.m. that delivery will be made. The third day is the delivery day. By 10:00 a.m. on this day the short must have in its account the Treasury issue that it specified on the notice day and by 1:00 p.m. must deliver that bond to the long that was assigned by the CBOT to accept delivery. The long pays the short the invoice price upon receipt of the bond.
2. Treasury Note Futures The three Treasury note futures contracts are 10-year, 5-year, and 2-year note contracts. All three contracts are modeled after the Treasury bond futures contract and are traded on the CBOT.
The underlying instrument for the 10-year Treasury note futures contract is $100,000 par value of a hypothetical 10-year, 6% Treasury note. Several acceptable Treasury issues may be delivered by the short. An issue is acceptable if the maturity is not less than 6.5 years and not greater than 10 years from the first day of the delivery month. Delivery options are granted to the short position.
For the 5-year Treasury note futures contract, the underlying is $100,000 par value of a 6% notional coupon U.S. Treasury note that satisfies the following conditions: (1) an original maturity of not more than 5 years and 3 months, (2) a remaining maturity no greater than 5 years and 3 months, and (3) a remaining maturity not less than 4 years and 2 months.
The underlying for the 2-year Treasury note futures contract is $200,000 par value of a 6% notional coupon U.S. Treasury note with a remaining maturity of not more than 2 years and not less than 1 year and 9 months. Moreover, the original maturity of the note delivered to satisfy the 2-year futures cannot be more than 5 years and 3 months.
3. Agency Note Futures Contract In 2000, the CBOT and the Chicago Mercantile Exchange (CME) began trading in futures contracts in which the underlying is a Fannie Mae or Freddie Mac agency debenture security. (Agency debentures are explained in Chapter 3.) The underlying for the CBOT 10-year agency note futures contract is a Fannie Mae benchmark note or Freddie Mac reference note having a par value of $100,000 and a notional coupon of 6%. The 10-year agency note futures contract of the CME is similar to that of the CBOT, but has a notional coupon of 6.5% instead of 6%.
As with the Treasury futures contract, more than one issue is deliverable for both the CBOT and CME agency note futures contract. The contract delivery months are March, June, September, and December. As with the Treasury futures contract a conversion factor applies to each eligible issue for each contract settlement date. Because many issues are deliverable, one issue is the cheapest-to-deliver issue. This issue is found in exactly the same way as with the Treasury futures contract.
III. INTEREST RATE OPTIONS
An option is a contract in which the writer of the option grants the buyer of the option the right, but not the obligation, to purchase from or sell to the writer something at a specified price within a specified period of time (or at a specified date). The writer, also referred to as the seller, grants this right to the buyer in exchange for a certain sum of money, called the option price or option premium. The price at which the underlying for the contract may be bought or sold is called the exercise price or strike price. The date after which an option is void is called the expiration date. Our focus is on options where the “something” underlying the option is an interest rate instrument or an interest rate.
When an option grants the buyer the right to purchase the designated instrument from the writer (seller), it is referred to as a call option, or call. When the option buyer has the right to sell the designated instrument to the writer, the option is called a put option, or put.
An option is also categorized according to when the option buyer may exercise the option. There are options that may be exercised at any time up to and including the expiration date. Such an option is referred to as an American option. There are options that may be exercised only at the expiration date. An option with this feature is called a European option. An option that can be exercised prior to maturity but only on designated dates is called a modified American, Bermuda, or Atlantic option.
A. Risk and Return Characteristics of Options
The maximum amount that an option buyer can lose is the option price. The maximum profit that the option writer can realize is the option price at the time of sale. The option buyer has substantial upside return potential, while the option writer has substantial downside risk.
It is assumed in this chapter that the reader has an understanding of the basic positions that can be created with options. These positions include:
1. long call position (buying a call option)
2. short call position (selling a call option)
3. long put position (buying a put option)
4. short put position (selling a put option)
Exhibit 3 shows the payoff profile for these four option positions assuming that each option position is held to the expiration date and not exercised early.
B. Differences Between Options and Futures Contracts
Unlike a futures contract, one party to an option contract is not obligated to transact. Specifically, the option buyer has the right, but not the obligation, to transact. The option writer does have the obligation to perform. In the case of a futures contract, both buyer and seller are obligated to perform. Of course, a futures buyer does not pay the seller to accept the obligation, while an option buyer pays the option seller an option price.
Consequently, the risk/reward characteristics of the two contracts are also different. In the case of a futures contract, the buyer of the contract realizes a dollar-for-dollar gain when the price of the futures contract increases and suffers a dollar-for-dollar loss when the price of the futures contract drops. The opposite occurs for the seller of a futures contract. Options do not provide this symmetric risk/reward relationship. The most that the buyer of an option can lose is the option price. While the buyer of an option retains all the potential benefits, the gain is always reduced by the amount of the option price. The maximum profit that the writer may realize is the option price; this is compensation for accepting substantial downside risk.
Both parties to a futures contract are required to post margin. There are no margin requirements for the buyer of an option once the option price has been paid in full. Because the option price is the maximum amount that the investor can lose, no matter how adverse the price movement of the underlying, there is no need for margin. Because the writer of an option has agreed to accept all of the risk (and none of the reward) of the position in the underlying, the writer is generally required to put up the option price received as margin. In addition, as price changes occur that adversely affect the writer’s position, the writer is required to deposit additional margin (with some exceptions) as the position is marked to market.
EXHIBIT 3 Payoff of Basic Option Positions if Held to Expiration Date
C. Exchange-Traded Versus OTC Options
Options, like other financial instruments, may be traded either on an organized exchange or in the over-the-counter (OTC) market. An exchange that wants to create an options contract must obtain approval from regulators. Exchange-traded options have three advantages. First, the strike price and expiration date of the contract are standardized.176 Second, as in the case of futures contracts, the direct link between buyer and seller is severed after the order is executed because of the interchangeability of exchange-traded options. The clearinghouse performs the same guarantor function in the options market that it does in the futures market. Finally, transaction costs are lower for exchange-traded options than for OTC options.
The higher cost of an OTC option reflects the cost of customizing the option for the many situations where an institutional investor needs to have a tailor-made option because the standardized exchange-traded option does not satisfy its investment objectives. Investment banking firms and commercial banks act as principals as well as brokers in the OTC options market. While an OTC option is less liquid than an exchange-traded option, this is typically not of concern to an institutional investor—most institutional investors use OTC options as part of an asset/liability strategy and intend to hold them to expiration.
Exchange-traded interest rate options can be written on a fixed income security or an interest rate futures contract. The former options are called options on physicals. For reasons to be explained later, options on interest rate futures are more popular than options on physicals. However, portfolio managers have made increasingly greater use of OTC options.
1. Exchange-Traded Futures Options There are futures options on all the interest rate futures contracts mentioned earlier in this chapter. An option on a futures contract, commonly referred to as a futures option, gives the buyer the right to buy from or sell to the writer a designated futures contract at the strike price at any time during the life of the option. If the futures option is a call option, the buyer has the right to purchase one designated futures contract at the strike price. That is, the buyer has the right to acquire a long futures position in the underlying futures contract. If the buyer exercises the call option, the writer acquires a corresponding short position in the same futures contract.
A put option on a futures contract grants the buyer the right to sell one designated futures contract to the writer at the strike price. That is, the option buyer has the right to acquire a short position in the designated futures contract. If the put option is exercised, the writer acquires a corresponding long position in the designated futures contract.
As the parties to the futures option will realize a position in a futures contract when the option is exercised, the question is: what will the futures price be? What futures price will the long be required to pay for the futures contract, and at what futures price will the short be required to sell the futures contract?
Upon exercise, the futures price for the futures contract will be set equal to the strike price. The position of the two parties is then immediately marked-to-market in terms of the then-current futures price. Thus, the futures position of the two parties will be at the prevailing futures price. At the same time, the option buyer will receive from the option seller the economic benefit from exercising. In the case of a call futures option, the option writer must pay the difference between the current futures price and the strike price to the buyer of the option. In the case of a put futures option, the option writer must pay the option buyer the difference between the strike price and the current futures price.
For example, suppose an investor buys a call option on some futures contract in which the strike price is 85. Assume also that the futures price is 95 and that the buyer exercises the call option. Upon exercise, the call buyer is given a long position in the futures contract at 85 and the call writer is assigned the corresponding short position in the futures contract at 85. The futures positions of the buyer and the writer are immediately marked-to-market by the exchange. Because the prevailing futures price is 95 and the strike price is 85, the long futures position (the position of the call buyer) realizes a gain of 10, while the short futures position (the position of the call writer) realizes a loss of 10. The call writer pays the exchange 10 and the call buyer receives from the exchange 10. The call buyer, who now has a long futures position at 95, can either liquidate the futures position at 95 or maintain a long futures position. If the former course of action is taken, the call buyer sells his futures contract at the prevailing futures price of 95. There is no gain or loss from liquidating the position. Overall, the call buyer realizes a gain of 10 (less the option purchase price). The call buyer who elects to hold the long futures position will face the same risk and reward of holding such a position, but still realizes a gain of 10 from the exercise of the call option.
Suppose instead that the futures option with a strike price of 85 is a put rather than a call, and the current futures price is 60 rather than 95. Then, if the buyer of this put option exercises it, the buyer would have a short position in the futures contract at 85; the option writer would have a long position in the futures contract at 85. The exchange then marks the position to market at the then-current futures price of 60, resulting in a gain to the put buyer of 25 and a loss to the put writer of the same amount. The put buyer now has a short futures position at 60 and can either liquidate the short futures position by buying a futures contract at the prevailing futures price of 60 or maintain the short futures position. In either case the put buyer realizes a gain of 25 (less the option purchase price) from exercising the put option.
There are no margin requirements for the buyer of a futures option once the option price has been paid in full. Because the option price is the maximum amount that the buyer can lose regardless of how adverse the price movement of the underlying instrument, there is no need for margin. Because the writer (seller) of a futures option has agreed to accept all of the risk (and none of the reward) of the position in the underlying instrument, the writer (seller) is required to deposit not only the margin required on the interest rate futures contract position but also (with certain exceptions) the option price that is received from writing the option.
The price of a futures option is quoted in 64ths of 1% of par value. For example, a price of 24 means of 1% of par value. Since the par value of a Treasury bond futures contract is $100,000, an option price of 24 means: [
/100] ×$100,000 = $375. In general, the price of a futures option quoted at Q is equal to:
/100] ×$100,000 = $375. In general, the price of a futures option quoted at Q is equal to:There are three reasons that futures options have largely supplanted options on fixed income securities as the options vehicle of choice for institutional investors who want to use exchange-traded options. First, unlike options on fixed income securities, options on Treasury coupon futures do not require payments for accrued interest to be made. Consequently, when a futures option is exercised, the call buyer and the put writer need not compensate the other party for accrued interest. Second, futures options are believed to be “cleaner” instruments because of the reduced likelihood of delivery squeezes. Market participants who must deliver an instrument are concerned that at the time of delivery the instrument to be delivered will be in short supply, resulting in a higher price to acquire the instrument. As the deliverable supply of futures contracts is infinite for futures options currently traded, there is no concern about a delivery squeeze. Finally, in order to price any option, it is imperative to know at all times the price of the underlying instrument. In the bond market, current prices are not as easily available as price information on the futures contract. The reason is that as bonds trade in the OTC market there is no single reporting system with recent price information. Thus, an investor who wanted to purchase an option on a Treasury bond would have to call several dealer firms to obtain a price. In contrast, futures contracts are traded on an exchange and, as a result, price information is reported.
2. Over-the-Counter Options Institutional investors who want to purchase an option on a specific Treasury security or a Ginnie Mae passthrough security can do so on an over-the-counter basis. There are government and mortgage-backed securities dealers who make a market in options on specific securities. OTC options, also called dealer options, usually are purchased by institutional investors who want to hedge the risk associated with a specific security. For example, a thrift may be interested in hedging its position in a specific mortgage passthrough security. Typically, the maturity of the option coincides with the time period over which the buyer of the option wants to hedge, so the buyer is not concerned with the option’s liquidity.
In the absence of a clearinghouse the parties to any over-the-counter contract are exposed to counterparty risk.177 In the case of forward contracts where both parties are obligated to perform, both parties face counterparty risk. In contrast, in the case of an option, once the option buyer pays the option price, it has satisfied its obligation. It is only the seller that must perform if the option is exercised. Thus, the option buyer is exposed to counterparty risk—the risk that the option seller will fail to perform.
OTC options can be customized in any manner sought by an institutional investor. Basically, if a dealer can reasonably hedge the risk associated with the opposite side of the option sought, it will create the option desired by a customer. OTC options are not limited to European or American type. Dealers also create modified American (Bermuda or Atlantic) type options.
IV. INTEREST RATE SWAPS
In an interest rate swap, two parties agree to exchange periodic interest payments. The dollar amount of the interest payments exchanged is based on some predetermined dollar principal, which is called the notional principal or notional amount. The dollar amount each counterparty pays to the other is the agreed-upon periodic interest rate times the notional principal. The only dollars that are exchanged between the parties are the interest payments, not the notional principal. In the most common type of swap, one party agrees to pay the other party fixed interest payments at designated dates for the life of the contract. This party is referred to as the fixed-rate payer. The fixed rate that the fixed-rate payer must make is called the swap rate. The other party, who agrees to make interest rate payments that float with some reference rate, is referred to as the fixed-rate receiver.
The reference rates that have been used for the floating rate in an interest rate swap are those on various money market instruments: Treasury bills, the London interbank offered rate, commercial paper, bankers acceptances, certificates of deposit, the federal funds rate, and the prime rate. The most common is the London interbank offered rate (LIBOR). LIBOR is the rate at which prime banks offer to pay on Eurodollar deposits available to other prime banks for a given maturity. Basically, it is viewed as the global cost of bank borrowing. There is not just one rate but a rate for different maturities. For example, there is a 1-month LIBOR, 3-month LIBOR, 6-month LIBOR, etc.
To illustrate an interest rate swap, suppose that for the next five years party X agrees to pay party Y 6% per year (the swap rate), while party Y agrees to pay party X 6-month LIBOR (the reference rate). Party X is the fixed-rate payer, while party Y is the fixed-rate receiver. Assume that the notional principal is $50 million, and that payments are exchanged every six months for the next five years. This means that every six months, party X (the fixed-rate payer) will pay party Y $1.5 million (6% times $50 million divided by 2).178 The amount that party Y (the fixed-rate receiver) will pay party X will be 6-month LIBOR times $50 million divided by 2. If 6-month LIBOR is 5% at the beginning of the 6-month period, party Y will pay party X $1.25 million (5% times $50 million divided by 2). Mechanically, the floating-rate is determined at the beginning of a period and paid in arrears—that is, it is paid at the end of the period. The two payments are actually netted out so that $0.25 million will be paid from party X to party Y. Note that we divide by two because one-half year’s interest is being paid. This is illustrated in panel a of Exhibit 4.
The convention that has evolved for quoting a swap rate is that a dealer sets the floating rate equal to the reference rate and then quotes the fixed rate that will apply. The fixed rate is the swap rate and reflects a “spread” above the Treasury yield curve with the same term to maturity as the swap. This spread is called the swap spread.
EXHIBIT 4 Summary of How the Value of a Swap to Each Counterparty Changes when Interest Rates Change
b. Interest rates increase such that swap rate is 7% for new swaps
Fixed-rate payer pays initial swap rate of 6% to obtain 6-month LIBOR
Advantage to fixed-rate payer: pays only 6% not 7% to obtain 6-month LIBOR
Fixed-rate receiver pays 6-month LIBOR
Disadvantage to fixed-rate receiver: receives only 6% in exchange for 6-month LIBOR, not 7%
Results of a rise in interest rates:
| Party | Value of swap |
|---|---|
| Fixed-rate payer | Increases |
| Fixed-rate receiver I | Decreases |
c. Interest rates decrease such that swap rate is 5% for new swaps
Fixed-rate payer pays initial swap rate of 6% to obtain 6-month LIBOR
Disadvantage to fixed-rate payer: must pay 6% not 5% to obtain 6-month LIBOR
Fixed-rate receiver pays 6-month LIBOR
Advantage to fixed-rate receiver: receives 6% in exchange for 6-month LIBOR, not 5%
Results of a decrease in interest rates:
| Party | Value of swap |
|---|---|
| Fixed-rate payer | Decreases |
| Fixed-rate receiver | I Increases |
A. Entering Into a Swap and Counterparty Risk
Interest rate swaps are OTC instruments. This means that they are not traded on an exchange. An institutional investor wishing to enter into a swap transaction can do so through either a securities firm or a commercial bank that transacts in swaps.179 These entities can do one of the following. First, they can arrange or broker a swap between two parties that want to enter into an interest rate swap. In this case, the securities firm or commercial bank is acting in a brokerage capacity. The broker is not a party to the swap.
The second way in which a securities firm or commercial bank can get an institutional investor into a swap position is by taking the other side of the swap. This means that the securities firm or the commercial bank is a dealer rather than a broker in the transaction. Acting as a dealer, the securities firm or the commercial bank must hedge its swap position in the same way that it hedges its position in other securities that it holds. Also it means that the dealer (which we refer to as a swap dealer) is the counterparty to the transaction. If an institutional investor entered into a swap with a swap dealer, the institutional investor will look to the swap dealer to satisfy the obligations of the swap; similarly, that same swap dealer looks to the institutional investor to fulfill its obligations as set forth in the swap.
The risk that the two parties take on when they enter into a swap is that the other party will fail to fulfill its obligations as set forth in the swap agreement. That is, each party faces default risk and therefore there is bilateral counterparty risk.
B. Risk/Return Characteristics of an Interest Rate Swap
The value of an interest rate swap will fluctuate with market interest rates. As interest rates rise, the fixed-rate payer is receiving a higher 6-month LIBOR (in our illustration). He would need to pay more for a new swap. Let’s consider our hypothetical swap. Suppose that interest rates change immediately after parties X and Y enter into the swap. Panel a in Exhibit 4 shows the transaction. First, consider what would happen if the market demanded that in any 5-year swap the fixed-rate payer must pay 7% in order to receive 6-month LIBOR. If party X (the fixed-rate payer) wants to sell its position to party A, then party A will benefit by having to pay only 6% (the original swap rate agreed upon) rather than 7% (the current swap rate) to receive 6-month LIBOR. Party X will want compensation for this benefit. Consequently, the value of party X’s position has increased. Thus, if interest rates increase, the fixed-rate payer will realize a profit and the fixed-rate receiver will realize a loss. Panel b in Exhibit 4 summarizes the results of a rise in interest rates.
Next, consider what would happen if interest rates decline to, say, 5%. Now a 5-year swap would require a new fixed-rate payer to pay 5% rather than 6% to receive 6-month LIBOR. If party X wants to sell its position to party B, the latter would demand compensation to take over the position. In other words, if interest rates decline, the fixed-rate payer will realize a loss, while the fixed-rate receiver will realize a profit. Panel c in Exhibit 4 summarizes the results of a decline in interest rates
While we know in what direction the change in the value of a swap will be for the counterparties when interest rates change, the question is how much will the value of the swap change. We show how to compute the change in the value of a swap in the next chapter.
C. Interpreting a Swap Position
There are two ways that a swap position can be interpreted: (1) a package of forward (futures) contracts and (2) a package of cash flows from buying and selling cash market instruments.
1. Package of Forward (Futures) Contracts Contrast the position of the counterparties in an interest rate swap summarized above to the position of the long and short interest rate futures (forward) contract. The long futures position gains if interest rates decline and loses if interest rates rise—this is similar to the risk/return profile for a floating-rate payer. The risk/return profile for a fixed-rate payer is similar to that of the short futures position: a gain if interest rates increase and a loss if interest rates decrease. By taking a closer look at the interest rate swap we can understand why the risk/return relationships are similar.
Consider party X’s position in our previous swap illustration. Party X has agreed to pay 6% and receive 6-month LIBOR. More specifically, assuming a $50 million notional principal, X has agreed to buy a commodity called “6-month LIBOR” for $1.5 million. This is effectively a 6-month forward contract where X agrees to pay $1.5 million in exchange for delivery of 6-month LIBOR. If interest rates increase to 7%, the price of that commodity (6-month LIBOR) is higher, resulting in a gain for the fixed-rate payer, who is effectively long a 6-month forward contract on 6-month LIBOR. The floating-rate payer is effectively short a 6-month forward contract on 6-month LIBOR. There is therefore an implicit forward contract corresponding to each exchange date.
Now we can see why there is a similarity between the risk/return relationship for an interest rate swap and a forward contract. If interest rates increase to, say, 7%, the price of that commodity (6-month LIBOR) increases to $1.75 million (7% times $50 million divided by 2). The long forward position (the fixed-rate payer) gains, and the short forward position (the floating-rate payer) loses. If interest rates decline to, say, 5%, the price of our commodity decreases to $1.25 million (5% times $50 million divided by 2). The short forward position (the floating-rate payer) gains, and the long forward position (the fixed-rate payer) loses.
Consequently, interest rate swaps can be viewed as a package of more basic interest rate derivatives, such as forwards.180 The pricing of an interest rate swap will then depend on the price of a package of forward contracts with the same settlement dates in which the underlying for the forward contract is the same reference rate. We will make use of this principle in the next chapter when we explain how to value swaps.
While an interest rate swap may be nothing more than a package of forward contracts, it is not a redundant contract for several reasons. First, maturities for forward or futures contracts do not extend out as far as those of an interest rate swap; an interest rate swap with a term of 15 years or longer can be obtained. Second, an interest rate swap is a more transactionally efficient instrument. By this we mean that in one transaction an entity can effectively establish a payoff equivalent to a package of forward contracts. The forward contracts would each have to be negotiated separately. Third, the interest rate swap market has grown in liquidity since its introduction in 1981; interest rate swaps now provide more liquidity than forward contracts, particularly long-dated (i.e., long-term) forward contracts.
2. Package of Cash Market Instruments To understand why a swap can also be interpreted as a package of cash market instruments, consider an investor who enters into the transaction below:
• buy $50 million par of a 5-year floating-rate bond that pays 6-month LIBOR every six months
• finance the purchase by borrowing $50 million for five years on terms requiring a 6% annual interest rate payable every six months
As a result of this transaction, the investor
• receives a floating rate every six months for the next five years
• pays a fixed rate every six months for the next five years
The cash flows for this transaction are set forth in Exhibit 5. The second column of the exhibit shows the cash flow from purchasing the 5-year floating-rate bond. There is a $50 million cash outlay and then ten cash inflows. The amount of the cash inflows is uncertain because they depend on future LIBOR. The next column shows the cash flow from borrowing $50 million on a fixed-rate basis. The last column shows the net cash flow from the entire transaction. As the last column indicates, there is no initial cash flow (no cash inflow or cash outlay). In all ten 6-month periods, the net position results in a cash inflow of LIBOR and a cash outlay of $1.5 million. This net position, however, is identical to the position of a fixed-rate payer/floating-rate receiver.
It can be seen from the net cash flow in Exhibit 5 that a fixed-rate payer has a cash market position that is equivalent to a long position in a floating-rate bond and a short position in a fixed-rate bond—the short position being the equivalent of borrowing by issuing a fixed-rate bond.
What about the position of a floating-rate payer? It can be easily demonstrated that the position of a floating-rate payer is equivalent to purchasing a fixed-rate bond and financing that purchase at a floating rate, where the floating rate is the reference rate for the swap. That is, the position of a floating-rate payer is equivalent to a long position in a fixed-rate bond and a short position in a floating-rate bond.
D. Describing the Counterparties to a Swap Agreement
The terminology used to describe the position of a party in the swap markets combines cash market jargon and futures market jargon, given that a swap position can be interpreted as a position in a package of cash market instruments or a package of futures/forward positions. As we have said, the counterparty to an interest rate swap is either a fixed-rate payer or floating-rate payer.
Exhibit 6 lists how the counterparties to an interest rate swap agreement are described.181 To understand why the fixed-rate payer is viewed as “short the bond market,” and the floating-rate payer is viewed as “long the bond market,” consider what happens when interest rates change. Those who borrow on a fixed-rate basis will benefit if interest rates rise because they have locked in a lower interest rate. But those who have a short bond position will also benefit if interest rates rise. Thus, a fixed-rate payer can be said to be short the bond market. A floating-rate payer benefits if interest rates fall. A long position in a bond also benefits if interest rates fall, so terminology describing a floating-rate payer as long the bond market is not surprising. From our discussion of the interpretation of a swap as a package of cash market instruments, describing a swap in terms of the sensitivities of long and short cash positions follows naturally.182
EXHIBIT 5 Cash Flow for the Purchase of a 5-Year Floating-Rate Bond Financed by Borrowing on a Fixed-Rate Basis
EXHIBIT 6 Describing the Parties to a Swap Agreement
| Fixed-rate payer | Fixed-rate receiver |
|---|---|
| • pays fixed rate in the swap | • pays floating rate in the swap |
| • receives floating in the swap | • receives fixed in the swap |
| • is short the bond market | • is long the bond market |
| • has bought a swap | • has sold a swap |
| • is long a swap | • is short a swap |
| • has established the price sensitivities of a longer-term fixed-rate liability and a floating-rate asset | • has established the price sensitivities of a longer-term fixed-rate asset and a floating-rate liability |
V. INTEREST RATE CAPS AND FLOORS
There are agreements between two parties whereby one party for an upfront premium agrees to compensate the other at specific time periods if the reference rate is different from a predetermined level. If one party agrees to pay the other when the reference rate exceeds a predetermined level, the agreement is referred to as an interest rate cap or ceiling. The agreement is referred to as an interest rate floor if one party agrees to pay the other when the reference rate falls below a predetermined level. The predetermined level is called the strike rate. The strike rate for a cap is called the cap rate; the strike rate for a floor is called the floor rate.
The terms of a cap and floor agreement include:
1. the reference rate
2. the strike rate (cap rate or floor rate) that sets the ceiling or floor
3. the length of the agreement
4. the frequency of settlement
5. the notional principal
For example, suppose that C buys an interest rate cap from D with the following terms:
1. the reference rate is 3-month LIBOR.
2. the strike rate is 6%.
3. the agreement is for four years.
4. settlement is every three months.
5. the notional principal is $20 million.
Under this agreement, every three months for the next four years, D will pay C whenever 3-month LIBOR exceeds 6% at a settlement date. The payment will equal the dollar value of the difference between 3-month LIBOR and 6% times the notional principal divided by 4. For example, if three months from now 3-month LIBOR on a settlement date is 8%, then D will pay C 2% (8% minus 6%) times $20 million divided by 4, or $100,000. If 3-month LIBOR is 6% or less, D does not have to pay anything to C.
In the case of an interest rate floor, assume the same terms as the interest rate cap we just illustrated. In this case, if 3-month LIBOR is 8%, C receives nothing from D, but if 3-month LIBOR is less than 6%, D compensates C for the difference. For example, if 3-month LIBOR is 5%, D will pay C $50,000 (6% minus 5% times $20 million divided by 4).183
A. Risk/Return Characteristics
In an interest rate agreement, the buyer pays an upfront fee which represents the maximum amount that the buyer can lose and the maximum amount that the seller (writer) can gain. The only party that is required to perform is the seller of the interest rate agreement. The buyer of an interest rate cap benefits if the reference rate rises above the strike rate because the seller must compensate the buyer. The buyer of an interest rate floor benefits if the reference rate falls below the strike rate, because the seller must compensate the buyer.
The seller of an interest rate cap or floor does not face counterparty risk once the buyer pays the fee. In contrast, the buyer faces counterparty risk. Thus, as with options, there is unilateral counterparty risk.
B. Interpretation of a Cap and Floor Position
In an interest rate cap and floor, the buyer pays an upfront fee, which represents the maximum amount that the buyer can lose and the maximum amount that the seller of the agreement can gain. The only party that is required to perform is the seller of the interest rate agreement. The buyer of an interest rate cap benefits if the reference rate rises above the strike rate because the seller must compensate the buyer. The buyer of an interest rate floor benefits if the reference rate falls below the strike rate because the seller must compensate the buyer.
How can we better understand interest rate caps and interest rate floors? In essence these contracts are equivalent to a package of interest rate options at different time periods. As with a swap, a complex contract can be seen to be a package of basic contracts—options in the case of caps and floors. Each of the interest rate options comprising a cap are called caplets; similarly, each of the interest rate options comprising a floor are called floorlets.
The question is what type of package of options is a cap and a floor. Note the following very carefully! It depends on whether the underlying is a rate or a fixed-income instrument. If the underlying is considered a fixed-income instrument, its value changes inversely with interest rates. Therefore:
• for a call option on a fixed-income instrument:
1. interest rates increase → fixed-income instrument’s price decreases → call option value decreases and
2. interest rates decrease → fixed-income instrument’s price increases → call option value increases
• for a put option on a fixed-income instrument
1. interest rates increase → fixed-income instrument’s price decreases → put option value increases and
2. interest rates decrease → fixed-income instrument’s price increases → put option value decreases
To summarize the situation for call and put options on a fixed-income instrument:
| When interest rates | ||
|---|---|---|
| Value of: | increase | decrease |
| long call | decrease | increase |
| short call | increase | decrease |
| long put | increase | decrease |
| short put | decrease | increase |
For a cap and floor, the situation is as follows
| When interest rates | ||
| Value of: | increase | decrease |
|---|---|---|
| short cap | decrease | increase |
| long cap | increase | decrease |
| short floor | increase | decrease |
| long floor | decrease | increase |
Therefore, buying a cap (long cap) is equivalent to buying a package of puts on a fixed-income instrument and buying a floor (long floor) is equivalent to buying a package of calls on a fixed-income instrument.
Caps and floors can also be seen as packages of options on interest rates. In the over-the-counter market one can purchase an option on an interest rate. These options work as follows in terms of their payoff. There is a strike rate. For a call option on an interest rate, there is a payoff if the reference rate is greater than the strike rate. This means that when interest rates increase, the call option’s value increases and when interest rates decrease, the call option’s value decreases. As can be seen from the payoff for a cap and a floor summarized above, this is the payoff of a long cap. Consequently, a cap is equivalent to a package of call options on an interest rate. For a put option on an interest rate, there is a payoff when the reference rate is less than the strike rate. When interest rates increase, the value of the put option on an interest rate decreases, as does the value of a long floor position (see the summary above); when interest rates decrease, the value of the put on an interest rate increases, as does the value of a long floor position (again, see the summary above). Thus, a floor is equivalent to a package of put options on an interest rate.
When market participants talk about the equivalency of caps and floors in terms of put and call options, they must specify the underlying. For example, a long cap is equivalent to a package of call options on interest rates or a package of put options on a fixed-income instrument.
C. Creation of an Interest Rate Collar
Interest rate caps and floors can be combined by borrowers to create an interest rate collar. This is done by buying an interest rate cap and selling an interest rate floor. The purchase of the cap sets a maximum interest rate that a borrower would have to pay if the reference rate rises. The sale of a floor sets the minimum interest rate that a borrower can benefit from if the reference rate declines. Therefore, there is a range for the interest rate that the borrower must pay if the reference rate changes. The net premium that a borrower who wants to create a collar must pay is the difference between the premium paid to purchase the cap and the premium received to sell the floor.
For example, consider the following collar created by a borrower: a cap purchased with a strike rate of 7% and a floor sold with a strike rate of 4%. If the reference rate exceeds 7%, the borrower receives a payment; if the reference rate is less than 4%, the borrower makes a payment. Thus, the borrower’s cost will have a range from 4% to 7%. Note, however, that the borrower’s effective interest cost is adjusted by the net premium that the borrower must pay.
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