Frank J. Fabozzi, Ph.D., CFA

Adjunct Professor of Finance School of Management Yale University

Steven V. Mann, Ph.D.

Professor of Finance The Moore School of Business University of South Carolina

The previous chapter covered the role of derivatives in portfolio management, the different types of derivatives, and the valuation of derivatives. In the description of the types of derivatives, the difference in the risk and return characteristics of futures-type products and option-type products was described, as well as the distinction between exchange-traded products and over-the-counter products. The focus in the previous chapter was on equity derivatives.

In this chapter we look at interest rate derivatives. We will not repeat the fundamental characteristics of derivatives. Instead, we will look at the derivative products available in the market for controlling interest rate risk. The chapter is divided into four sections for each type of derivative: futures/forward contracts, options, swaps, and caps/floors.

INTEREST RATE FUTURES

A futures contract is an agreement that requires each party to the agreement either to buy or sell something at a designated future date at a predetermined price. 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to interim cash flows as additional margin may be required in the case of adverse price movements, or as cash is withdrawn, in the case of favorable price movements.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.

Below we discuss these two types of contracts in which the underlying is a fixed-income security or an interest rate. We begin with interest rate futures contracts, which can be classified by the maturity of their underlying security. Interest rate futures on short-term instruments have an underlying security that matures in one year or less. The maturity of the underlying security of futures contracts on long-term instruments exceeds one year. We then discuss a forward rate agreement. We will discuss another important futures contract, a swap futures, later in this chapter when we cover interest rate swaps.

Interest Rate Futures on Short-Term Instruments

The three interest rate futures contracts on short-term instruments traded in the United States are the U.S. Treasury bill futures contract, the Eurodollar CD futures contract, and the federal funds futures contract. We discuss each in the following sections.

U.S. Treasury Bill Futures

The underlying for the Treasury bill futures contract, traded on the International Monetary Market (IMM) of the Chicago Mercantile Exchange, is a 13-week (3-month) Treasury bill with a face value of $1 million. More specifically, the seller of a Treasury bill futures contract agrees to deliver to the buyer on the settlement date a Treasury bill with 13 weeks remaining to maturity and a face value of $1 million. The Treasury bill delivered can be newly issued or seasoned. The futures price is the price at which the Treasury bill will be sold by the short and purchased by the long. For example, a Treasury bill futures contract that settles in 3 months requires that 3 months from now the short deliver to the long $1 million face value of a Treasury bill with 13 weeks remaining to maturity. The Treasury bill delivered could be a newly issued 13-week Treasury bill or a Treasury bill that was issued six months prior to the settlement date and therefore has only 13 weeks remaining until maturity.

Eurodollar CD Futures

As discussed in Chapter 6, Eurodollar certificates of deposit (CDs) are denominated in dollars but represent the liabilities of banks outside the United States. The contracts are traded on the International Monetary Market of the Chicago Mercantile Exchange and the London International Financial Futures Exchange (LIFFE). The rate paid on Eurodollar CDs is the London interbank offered rate (LIBOR).

The 3-month (90 day) Eurodollar CD is the underlying instrument for the Eurodollar CD futures contract. As with the Treasury bill futures contract, this contract is for $1 million of face value and is traded on an index price basis. The index price basis in which the contract is quoted is equal to 100 minus the annualized futures LIBOR. For example, a Eurodollar CD futures price of 98.00 means a futures 3-month LIBOR of 2%.

The Eurodollar CD futures contract is a cash settlement contract. Specifically, the parties settle in cash for the value of a Eurodollar CD based on LIBOR at the settlement date. The Eurodollar CD futures contract is one of the most heavily traded futures contracts in the world.

The Eurodollar CD futures contract is used frequently to trade the short end of the yield curve and many risk managers believe this contract to be the best hedging vehicle for a wide range of hedging situations.

Fed Funds Futures Contract

When the Federal Reserve formulates and executes monetary policy, the federal funds rate is frequently a significant operating target. Accordingly, the federal funds rate is a key short-term interest rate. The federal funds futures contract is designed for hedgers who have exposure to this rate or speculators who want to make a bet on the direction of U.S. monetary policy. Underlying this contract is the simple average overnight federal funds rate (i.e., the effective rate) for the delivery month. As such, this contract is settled in cash.

Interest Rate Futures on Long-Term Instruments

Interest rate futures on long-term instruments include Treasury bond and note futures, Agency note futures, and long-term municipal bond futures.

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, 6% coupon bond. The 6% coupon rate on the hypothetical bond is called the “notional coupon.”

We referred to the underlying as a hypothetical Treasury bond. The seller of a Treasury bond futures contract who decides to make delivery rather than liquidate a position by buying back the contract prior to the settlement date must deliver some Treasury bond. But what Treasury bond? The CBOT allows the seller to deliver one of several Treasury bonds that the CBOT specifies are acceptable for delivery. The CBOT makes its determination of the Treasury issues that are acceptable for delivery from all outstanding Treasury issues that have at least 15 years to maturity from the first day of the delivery month. Exhibit 29.1 shows the eligible issues as of August 30, 2001 for the June 2002 Treasury bond futures contract.

It is important to remember that while 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 as is the case of the equity index futures and the Eurodollar CD futures. The only way to close out a Treasury bond futures contract is to either initiate an offsetting futures position, or to deliver a Treasury issue that is acceptable for delivery.

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 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.

Source: Chicago Board of Trade

To make delivery equitable to both parties, the CBOT uses conversion factors for adjusting the price of each Treasury issue that can be delivered to satisfy the Treasury bond futures contract. Exhibit 29.1 shows for each of the acceptable Treasury issues for the June 2002 futures contract the corresponding conversion factor. The conversion factor is constant throughout the life of the futures contract.

Given the conversion factor for an issue and the futures price, the adjusted price is found by multiplying the conversion factor by the futures price. The adjusted price is called the converted price. 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

Cheapest-to-Deliver Issue

In selecting the issue to be delivered, the short will select from among all the deliverable issues the one that will give the largest rate of return from a cash-and-carry trade. A cash-and-carry trade is one in which a cash bond that is acceptable for delivery is purchased with borrowed funds and simultaneously the Treasury bond futures contract is sold. The bond purchased can be delivered to satisfy the short futures position. Thus, by buying the Treasury issue that is acceptable for delivery and selling the futures, an investor has effectively sold the bond at the delivery price (i.e., the converted price). A rate of return can be calculated for this trade. This rate of return is referred to as the implied repo rate.

Once the implied repo rate is calculated for each deliverable issue, the issue selected 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). The issue with the highest return is referred to as the cheapest-to-deliver issue and this issue plays a key role in the pricing of a Treasury futures contract. While an issue may be the cheapest-to-deliver issue today, changes in factors may cause some other issue to be the cheapest-to-deliver issue at a future date.

Other Delivery Options

In addition to the choice of which acceptable Treasury issue to deliver—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.

Treasury Note Futures

There are three Treasury note futures contracts: 10-year, 5-year, and 2-year. 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. There are several acceptable Treasury issues that 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. The 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 five years and three months, (2) a remaining maturity no greater then five years and three months, and (3) a remaining maturity not less than four years and two 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 two years and not less than one year and nine months. Moreover, the original maturity of the note delivered to satisfy the 2-year futures cannot be more than five years and three months.

Agency Note Futures Contract

The CBOT and the Chicago Mercantile Exchange (CME) trade futures contracts in which the underlying is a Fannie Mae or Freddie Mac agency debenture. (As explained in Chapter 9, Fannie Mae and Freddie Mac are government sponsored enterprises.) 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%. As with the Treasury futures contract, there is more than one issue that is deliverable and there is a conversion factor for each eligible issue. Because there are many issues that are deliverable, there is a cheapest-to-deliver issue.

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%. For an issue to be deliverable, the CME requires that the original maturity is 10 years and which does not mature for a period of at least 6.5 years from the date of delivery.

The CBOT and the CME also have a 5-year Agency note futures contract. Again, the CBOT’s underlying is a 6% notional coupon and the CME’s is a 6.5% notional coupon.

Long-Term Municipal Bond Index Futures Contract

The long-term municipal bond index futures contract is traded on the CBOT and is based on the value of the Bond Buyer Index (BBI) which consists of 40 municipal bonds. Unlike the Treasury bond futures contract, where the underlying to be delivered is $100,000 of a hypothetical 6% 20-year Treasury bond, the municipal bond index futures contract does not specify a par amount for the underlying index to be delivered. Instead, the dollar value of a futures contract is equal to the product of the futures price and $1,000. The settlement price on the last day of trading is equal to the product of the Bond Buyer Index value and $1,000. Since delivery on all 40 bonds in the index would be difficult, the contract is a cash settlement contract. This is unlike the Treasury bond futures contract which requires physical delivery of an acceptable Treasury bond issue.

In order to understand this futures contract, it is necessary to understand the nuances of how the BBI is constructed. The BBI consists of 40 actively traded general obligation and revenue bonds. To be included in the BBI, the following criteria must be satisfied: (1) the issue must have a Moody’s rating of A or higher and/or an S&P rating of A-or higher, and (2) the size of the term portion of the issue must be at least $50 million ($75 million for housing issues). No more than two bonds of the same issuer may be included in the BBI. In addition, for an issue to be considered, it must meet the following three conditions: (1) have at least 19 years remaining to maturity, (2) have a first call date between 7 and 16 years, and (3) have at least one call at par prior to redemption.

The Bond Buyer serves as the index manager for the contract and prices each issue in the index based on prices received daily from at least four of six dealer-to-dealer brokers. After dropping the highest price and the lowest price obtained for each issue, the average of the remaining prices is computed. This price is then used to calculate the BBI as follows. First, the price for an issue is multiplied by a conversion factor, just as in the case of the Treasury bond futures contract. This gives a converted price for each bond in the BBI. The converted prices for the bonds in the index are then summed and divided by 40, giving an average converted price for the BBI.

Finally, because the BBI is revised bimonthly when newer issues are added and older issues, or issues that no longer meet the criteria for inclusion in the index are dropped, a “smoothing coefficient” is calculated on the index revision date so that the value of the BBI will not change due merely to the change in its composition. The average converted price for the BBI is multiplied by this coefficient to get the value of the BBI for a particular date.

Nuances Associated with the Valuation of Futures Contracts

In the previous chapter, the valuation of stock index futures contracts is explained. Specifically, for stock index futures, the theoretical futures price is

Futures price = Spot price + Cost of financing - Dividend yield

For an interest rate futures contract, the first modification is to substitute cash yield on the underlying bond for the dividend yield. That is,

Futures price = Spot price + Cost of financing - Cash yield

Further modifications are necessary due to the nuances of specific interest rate futures contracts, particularly those that grant the short various options. Specifically, in deriving the theoretical futures price it is assumed that only one instrument is deliverable. But as explained earlier, the futures contract on Treasury bonds and notes and Agency Notes are designed to allow the short the choice of delivering one of a number of deliverable issues (the quality or swap option). Because there may be more than one deliverable, market participants track the price of each deliverable bond and determine which issue is the cheapest to deliver. The theoretical futures price will then trade in relation to the cheapest-to-deliver issue.

There is the risk that while an issue may be the cheapest to deliver at the time a position in the futures contract is taken, it may not be after that time. A change in the cheapest-to-deliver issue can dramatically alter the futures price. Because the swap option is an option granted by the long to the short, the long will want to pay less for the futures contract.

Therefore, as a result of the swap option, the theoretical futures price must be modified as follows:

Futures price = Spot price + Cost of financing - Cash yield - Value of the swap option

Market participants have employed theoretical models in attempting to estimate the fair value of the swap option.

Moreover, a known delivery date is assumed. As explained earlier, for the Treasury bond and note futures contracts, the short has a timing and wild card option, so the long does not know when the securities will be delivered. The effect of the timing and wild card options on the theoretical futures price is the same as with the swap option. These delivery options result in a theoretical futures price as follows:

Futures price = Spot price + Cost of financing - Cash yield - Value of the delivery options

Forward Rate Agreements

A forward rate agreement (FRA) is the over-the-counter equivalent of the exchange-traded futures contracts on short-term rates. Typically, the short-term rate is LIBOR.

The elements of an FRA are the contract rate, reference rate, settlement rate, notional amount, and settlement date. The parties to an FRA agree to buy and sell funds on the settlement date. The contract rate is the rate specified in the FRA at which the buyer of the FRA agrees to pay for funds and the seller of the FRA agrees to receive for investing funds. The reference rate is the interest rate used. The benchmark from which the interest payments are to be calculated is specified in the FRA and is called the notional amount (or notional principal). This amount is not exchanged between the two parties. The settlement rate is the value of the reference rate at the FRA’s settlement date. The source for determining the settlement rate is specified in the FRA.

The buyer of the FRA is agreeing to pay the contract rate, or equivalently, to buy funds on the settlement date at the contract rate; the seller of the FRA is agreeing to receive the contract rate, or equivalently to sell funds on the settlement date at the contract rate. So, for example, if the FRA has a contract rate of 5% for 3-month LIBOR (the reference rate) and the notional amount is $10 million, the buyer is agreeing to pay 5% to buy or borrow $10 million at the settlement date and the seller is agreeing to receive 5% to sell or lend $10 million at the settlement date.

If at the settlement date the settlement rate is greater than the contract rate, the FRA buyer benefits because the buyer can borrow funds at a below-market rate. If the settlement rate is less than the contract rate, this benefits the seller who can lend funds at an above-market rate. If the settlement rate is the same as the contract rate, neither party benefits. This is summarized below:

FRA buyer benefits if settlement rate > contract rate

FRA seller benefits if contract rate > settlement rate

Neither party benefits if settlement rate = contract rate

FRAs are cash settlement contracts. At the settlement date, the party that benefits based on the contract rate and settlement rate must be compensated by the other. Assuming the settlement rate is not equal to the contract rate then:

buyer receives compensation if settlement rate > contract rate

seller receives compensation if contract rate > settlement rate

To determine the amount that one party must compensate the other, the following is first calculated assuming a 360 day-count convention:

If settlement rate > contract rate:

Interest differential = (Settlement rate - Contract rate) x (Days in contract period/360) × Notional amount

If contract rate > settlement rate:

Interest differential = (Contract rate - Settlement rate) × (Days in contract period/360) × Notional amount

The amount that must be exchanged at the settlement is not the interest differential. Instead, the present value of the interest differential is exchanged. The discount rate used to calculate the present value of the interest differential is the settlement rate. Thus, the compensation is determined as follows:

To illustrate, assume the following terms for an FRA: reference rate is 3-month LIBOR, the contract rate is 5%, the notional amount is $10 million, and the number of days to settlement is 91 days. Suppose the settlement rate is 5.5%. This means that the buyer benefits since the buyer can borrow at 5% (the contract rate) when the market rate (the settlement rate) is 5.5%. Then

Interest differential = (0.055 - 0.05) × (91/360) × $10,000,000 = $12,638.89

The compensation or payment that the seller must make to the buyer is:

It is important to note the difference as to which party benefits when interest rates move in an FRA and a futures contract. The buyer of an FRA benefits if the reference rate increases and the seller benefits if the reference rate decreases. In a futures contract, the buyer benefits from a falling rate while the seller benefits from a rising rate. This is summarized below

This is because the underlying for each of the two contracts is different. In the case of an FRA, the underlying is a rate. The buyer gains if the rate increases and loses if the rate decreases. The opposite occurs for the seller of an FRA. In contrast, in a futures contract the underlying is a fixed-income instrument. The buyer gains if the fixed-income instrument increases in value. This occurs when rates decline. The buyer loses when the fixed-income instrument decreases in value. This occurs when interest rates increase. The opposite occurs for the seller of a futures contract.

The liquid and easily accessible sector of the FRA market is for 3-month and 6-month LIBOR. Rates are widely available for settlement starting one month forward, and settling once every month thereafter out to about six months forward. Thus, for example, on any given day forward rates are available for both 3-month and 6-month LIBOR one month forward, covering, respectively, the interest period starting in one month and ending in four months and the interest period staring in one month and ending in seven months. These contracts are referred to as 1x4 and 1x7 contracts. On the same day, there will be FRAs on 3-month and 6-month LIBOR for settlement two months forward. These are the 2x5 and 2x8 contracts. Similarly, settlements occur three months, four months, five months, and six months forward for both 3-month LIBOR and 6-month LIBOR. These contracts are also denoted by the beginning and ending of the interest period that they cover.

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, which is 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 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 a fixed income instrument or an interest rate.

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. Options on interest rate futures have been far more popular than options on physicals. However, institutional investors have made increasingly greater use of over-the-counter options.

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 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 establish a position in a futures contract when the option is exercised, the question is: What will the futures price be? That is, at what futures price will the long be required to pay for the instrument underlying the futures contract, and at what futures price will the short be required to sell the instrument underlying 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 and 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 a 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. 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 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 who now has a short futures position at 60 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 from exercising the put option.

There are three reasons why futures options on fixed income securities have largely supplanted options on physicals 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. Because the deliverable supply of futures contracts is more than adequate 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 because bonds trade in the over-the-counter market, there is no 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.

Over-the-Counter Options

Institutional investors who want to purchase an option on a specific Treasury security or a mortgage 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. Over-the-counter options, also called dealer options, usually are purchased by institutional investors who want to hedge the risk associated with a specific 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. 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, only the option buyer is exposed to counterparty risk.

OTC options can be customized in any manner sought by an institutional investor. Basically, if a dealer can 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. An option can be created in which the option can be exercised at several specified dates as well as the expiration date. Such options are referred to as modified American options, Bermuda options, and Atlantic options.

INTEREST RATE SWAPS

Interest rate swaps are over-the-counter instruments. 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, the notional principal. 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 other party, who agrees to make interest rate payments that float with some reference rate, is referred to as the fixed-rate receiver. Such swaps are referred to as fixed-for-floating rate swaps. 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 LIBOR.

To illustrate an interest rate swap, suppose that for the next five years party X agrees to pay party Y 6% per year, while party Y agrees to pay party X 3-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 three months for the next five years. This means that every three months, party X (the fixed-rate payer) will pay party Y $750,000 (6% times $50 million divided by 4). The amount that party Y (the fixed-rate receiver) will pay party X will be 3-month LIBOR times $50 million divided by 4. If 3-month LIBOR is 4%, party Y will pay party X $500,000 (4% times $50 million divided by 4).

The convention that has evolved for quoting swaps levels is that a swap dealer sets the floating rate equal to the reference rate and then quotes the fixed rate that will apply. The fixed rate is some spread above the Treasury yield curve with the same term to maturity as the swap. The fixed rate is called the swap rate. In our illustration above, the swap rate is 6%. The spread over the Treasury yield curve is called the swap spread.

The notional principal for the swap need not be the same amount over the life of the swap. That is, the notional principal can change. A swap in which the notional principal decreases over time is called an amortizing swap. A swap in which the notional principal increases over time is called an accreting swap.

There are swaps where both parties pay a floating interest rate. Such swaps are referred to as basis swaps.

Risk/Return Characteristics of an Interest Rate Swap

Because a swap is an OTC instrument, the risk that the two parties take on when they enter into a swap is that the counterparty will fail to fulfill its obligations. That is, each party faces default risk and therefore there is bilateral counterparty risk.

The value of an interest rate swap will change over time. To see how, let’s consider our hypothetical swap. Suppose that immediately after parties X and Y enter into the swap, the swap rate changes. First, consider what would happen if the swap rate for a 5-year swap increases from 6% to 8% (i.e., interest rates have increased). 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 swap rate specified in the contract) rather than 8% (the prevailing swap rate) to receive 3-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.

Next, consider what would happen if interest rates decline and the swap rate declines to, say, 5%. Now a 5-year swap would require a fixed-rate payer to pay 5% rather than 6% to receive 3-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.

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.

Package of Forward Contracts

Contrast the position of the counterparties in an interest rate swap described previously 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 fixed-rate receiver. 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. The reason is that an interest rate swap can be viewed as a package of more basic interest rate derivatives, such as forwards. 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.

Package of Cash Market Instruments

An interest rate swap is equivalent to a leveraged position in an asset. Specifically, it can be demonstrated that the position of a fixed-rate payer is equivalent to buying a floating-rate asset (i.e., receiving a floating-rate payment) and financing the purchase of that asset by issuing a fixed-rate bond (i.e., making a fixed-rate payment). For a fixed-rate receiver, the cash flow is identical to buying a fixed-rate asset and financing that purchase by issuing a floating-rate bond. That is why the two legs of a swap are referred to as the financing leg and asset leg.

Swaptions

There are options on interest rate swaps. These derivative contracts are called swaptions and grant the option buyer the right to enter into an interest rate swap at a future date. The time until expiration of the swap, the term of the swap, and the swap rate are specified. The swap rate is the strike rate for the option.

A payer’s swaption entitles the option buyer to enter into an interest rate swap in which the buyer of the option pays a fixed rate and receives a floating rate. Suppose that the strike rate is 6.5%, the term of the swap is three years, and the swaption expires in two years. This means that the buyer of this option some time over the next two years has the right to enter into a 3-year interest rate swap where the buyer pays 6.5% (the swap rate which is equal to the strike rate) and receives the reference rate.

In a receiver’s swaption the buyer of the option has the right to enter into an interest rate swap to pay a floating rate and receive a fixed rate. For example, if the strike rate is 7%, the swap term is five years, and the option expires in one year, the buyer of a receiver’s swaption has the right some time over the next year to enter into a 5-year interest rate swap in which the buyer receives a swap rate of 7% (i.e., the strike rate) and pays the reference rate.

Swap Futures Contract

The CBOT introduced a swap futures contract in late October 2001. The underlying instrument is the notional price of the fixed-rate side of a 10-year interest rate swap that has a notional principal equal to $100,000 and that exchanges semiannual interest payments at a fixed annual rate of 6% for floating interest rate payments based on 3-month LIBOR. This swap futures contract is cash settled with a settlement price determined by the International Swap and Derivatives Dealer (ISDA) benchmark 10-year swap rate on the last day of trading before the contract expires. This benchmark rate is published with a one-day lag in the Federal Reserve Board’s statistical release H.15.

INTEREST RATE CAPS AND FLOORS

An interest rate agreement is an agreement 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. When 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. The agreement is referred to as an interest rate floor when 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 terms of an interest rate agreement include:

1. The reference rate
2. The strike 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 party C buys an interest rate cap from party D with terms as follows:

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, party D will pay party C whenever 3-month LIBOR exceeds 6% at a settlement date. (Actually the payment is made arrears.). 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 party D will pay party C 2% (8% minus 6%) times $20 million divided by 4, or $100,000. If 3-month LIBOR is 6% or less, party D does not have to pay anything to party 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%, party C receives nothing from party D, but if 3-month LIBOR is less than 6%, party D compensates party C for the difference. For example, if 3-month LIBOR is 5%, party D will pay party C $50,000 (6% minus 5% times $20 million divided by 4).

Interest rate caps and floors can be combined to create an interest rate collar. This is done by buying an interest rate cap and selling an interest rate floor.

Risk/Return Characteristics

In an interest rate cap or floor, 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 cap or floor. 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.

To better understand interest rate caps and interest rate floors, we can look at them as in essence equivalent to a package of interest rate options. Since the buyer benefits if the interest rate rises above the strike rate, an interest rate cap is similar to purchasing a package of call options on the reference rate; the seller of an interest rate cap has effectively sold a package of these options. The buyer of an interest rate floor benefits from a decline in the reference rate below the strike rate. Therefore, the buyer of an interest rate floor has effectively bought a package of put options on the reference rate from the seller. An interest rate collar is equivalent to buying a package of call options and selling a package of put options. Once again, a complex contract can be seen to be a package of basic contracts, options in the case of interest rate agreements.

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.