FRANK J. FABOZZI, PhD, CFA, CPA
Professor in the Practice of Finance, Yale School of Management
STEVEN V. MANN, PhD
Professor of Finance, Moore School of Business, University of South Carolina
MOORAD CHOUDHRY, PhD
Head of Treasury, KBC Financial Products, London
Abstract: Interest rate options and related option-type products are used by market participants to control interest rate risk. There are exchange-traded and over-the-counter interest rate options. The interest rate options product most traded on exchanges is a futures option. Over-the-counter options include options on specific securities, spread options, compound options, caps, and floors. With all over-the-counter products there is counterparty risk faced by the buyer of the option or option-related product.
Keywords: option, American option, European option, Bermudan option, exotic options, nonstandard options, exchange-traded options, over-the-counter options, dealer options, futures options, counterparty risk, spread options, compound option, split-fee option, front fee, back fee, cap, floor, caplets, captions, flotions
An interest rate option is a derivative instrument that differs from an interest rate forward contract, a futures contract, and a swap in terms of its risk and return characteristics. As such, an interest rate option can be employed to control interest rate risk in ways that are either not possible or too costly to achieve using forwards, futures, or swaps. Options, like most other financial instruments, can be traded either on an organized exchange or in an over-the-counter (OTC) market. We begin the chapter with a basic description of an option and then go on to describe exchange-traded interest rate options. The most popular form of an exchange-traded option is an option on a futures contract. We then examine the various types of OTC options and derivative instruments with option-like features.
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 on 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. In effect, the writer is selling a promise in exchange for the option price. Conversely, the buyer pays the option price to obtain the writer's promise. The price at which the underlying 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 in this chapter is on options where the "something" underlying the option is an interest rate instrument.
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 on the expiration date. An option with this feature is called a European option. There are also Bermudan options, which are hybrids between American and European option contracts. The distinguishing feature of a Bermudan option contract is that early exercise is possible but is restricted to certain dates in the option's life.
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. The option buyer has substantial upside return potential, while the option writer faces substantial downside risk.
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 instrument, 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 instrument, 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.
Notice that, unlike in 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, the buyer of a futures contract does not pay the seller to accept the obligation, while an option buyer pays the seller the option price.
Consequently, the risk and 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 symmetric payoffs. 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 offset against substantial downside risk. This difference is extremely important because managers can use futures to protect against symmetric risk and options to protect against asymmetric risk.
There are exchange-traded options and over-the-counter options. Exchange-traded options have two advantages. First, the exercise price and expiration date of the contract are standardized. 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 associated with the exchange where the option trades performs the same function in the options market that it does in the futures market.
OTC options are used in the many situations where an institutional investor needs to have a customized 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.
OTC options can be customized in any manner sought by an institutional investor. There are plain vanilla options such as options on a specific Treasury issue. The more complex OTC options created are called exotic options or nonstandard options. Examples of OTC options are given later in this chapter. While an OTC option is less liquid than an exchange-traded option, this is typically not of concern since institutional investors who use OTC options as part of a hedging or asset/liability strategy intend to hold them to expiration.
In the absence of a clearinghouse, the parties to any OTC contract are exposed to counterparty risk. In the case of a forward contract (an OTC contract), both parties face counterparty risk since both parties are obligated to perform. Thus, there is bilateral counterparty risk. In contrast, for an OTC 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 unilateral counterparty risk—the risk that the option seller will fail to perform.
The underlying for an interest rate option can be a fixed income security or an interest rate futures contract. The former options are called options on physicals. In the United States, there are no actively exchange-traded options on physicals. Options on interest rate futures are called futures options. The actively traded interest rate options on exchanges are futures options.
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 designated 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 a 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.
Because 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? That is, at what price will the long be required to pay for the instrument underlying the futures contract, and at what 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 a 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 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.
OTC interest rate options are created by commercial banks and investment banks for their clients. Dealers can customize the expiration date, the underlying, and the type of exercise. For example, the underlying could be a specific fixed income security or a spread between yields in two sectors of the fixed income market.
In addition to American- and European-type options, an OTC option can be created in which the buyer may exercise prior to the expiration date but only on designated dates. As noted, such options are referred to as Bermuda options. With an OTC option, the buyer need not pay the option price at the time of purchase. Instead, the option price can be paid at the expiration or exercise date. For such options, the option writer, as well as the option buyer, is exposed to counterparty risk.
In the OTC option market, there are plain vanilla and exotic options. Plain vanilla options are options on specific securities or on the spread between two sectors of the bond market. Exotic options have more complicated payoffs, and we do not review these in this chapter.
Institutional investors who want to purchase an option on a specific Treasury security or a Ginnie Mae pass-through can do so on an OTC basis. There are government and mortgage-backed securities (MBS) dealers who make a market in options on specific securities. OTC or dealer options typically are purchased by institutional investors or mortgage bankers 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 usually not concerned with the option's liquidity.
A popular option used by mortgage originators for hedging forward delivery is an option on a specific MBS. Typically, the underlying security is a TBA (pools to be announced) agency pass-through security (Ginnie Mae, Fannie Mae, or Freddie Mac). The settlement process in the MBS market is forward delivery. The exercise of a mortgage option means the delivery of that security in the month specified in the option. Options are of the European type
Some institutional investors may have exposure not only to the level of rates but the spread between two yields. It is difficult to hedge against spread risk with current exchange-traded options. As a result, several dealer firms have developed proprietary products for such purpose. These options can be structured with a payoff in one of the following ways should the option expire in-the-money. First, there could be a cash settlement based on the amount that the option expires in-the-money. Second, there could be an exchange of ownership of the two securities underlying the option. It is difficult to structure options with a settlement based on an exchange of securities, but there are institutional investors who desire this type of structure.
Next, we discuss two types of spread options—an option on the yield curve and an option on the spread between MBS and Treasury securities.
Yield Curve Spread Option
The reason for the popularity of yield curve spread options is that there are many institutional investors whose performance is affected by a change in the shape of the yield curve. As an example of a yield curve spread option, consider the Goldman Sachs' product called SYCURVE. This option represents the right to buy (in the case of a call option) or sell (in the case of a put option) specific segments of the yield curve. "Buying the curve" means buying the shorter maturity and selling the longer maturity; "selling the curve" means selling the shorter maturity and buying the longer maturity. The curve is defined by the spread between two specific maturities. They could be the 2-year/10-year spread, the 2-year/30-year spread, or the 10-year/30-year spread. The strike is quoted in basis points.
The yield spread is measured by the long maturity yield minus the short maturity yield. For a call option to be in-the-money at the expiration date, the yield spread must be positive; for a put option to be in the money at the expiration date, the yield spread must be negative. For example, a 25-basis-point call option on the 2-year/10-year spread will be in-the-money at the expiration date if:
| 10-year yield – 2-year yield > 25 basis points |
A 35-basis-point put option on the 10-year/30-year spread will be in-the-money at the expiration date if:
| 30-year yield – 10-year yield < 35 basis points |
Yield curve options such as the SYCURVE are cash settlement contracts. In the case of the SYCURVE, if the option expires in-the-money, the option buyer receives $0.01 per $1 of notional amount, per in-the-money basis point at exercise. That is:
| Amount option expires in-the-money (in basis points) |
| × $0.01 × notional amount |
For example, suppose that $10 million notional amount of a 2-year/10-year call is purchased with a strike of 25 basis points. Suppose at the expiration date the yield spread is 33 basis points. Then the option expires 8 basis points in-the-money. The cash payment to the buyer of this option is
| 8 × $0.01 × $10,000,000 = $800,000 |
From this amount, the option price must be deducted.
MBS/Treasury Spread Option
Some institutional investors seek to control the spread risk between the yield on MBSs and Treasuries. One example of an option on this spread is Goldman Sachs's MOTTO (mortgages over Treasury) option. The buyer of a MOTTO call option benefits if MBSs outperform Treasuries; the buyer of a MOTTO put option benefits if Treasuries outperform MBSs.
As noted earlier in discussing MBS options, the structuring of MOTTO options is complicated by the nuances of the MBS market. For the particular Treasury, the calculation of its yield at the expiration date is straightforward given its price at the expiration date. However, at the expiration date, while the market price of a generic agency MBS with a given coupon rate is known, its yield is not uniquely determined. The yield depends on the prepayment assumption, which determines the particular security's cash flow. This yield is called the cash-flow yield, and the prepayment assumption is commonly called the prepayment speed. Each MBS dealer has a proprietary prepayment model to project the speed. One important factor in a prepayment model is the yield level relative to the coupon rate paid on the mortgages in the underlying mortgage pool. Thus, the yield on an MBS depends on the prepayment speed, which, in turn, depends on the yield level.
One possible way to handle this problem is to specify at the outset of the option the prepayment speed that should be used to determine the yield on an MBS given the Treasury yield at the expiration date. Specifically, the higher the Treasury yield, the lower the prepayment speed. However, it is not only the yield level but also the shape of the yield curve that affects the prepayment speed. Structuring a MOTTO such that the prepayment speed for all possible combinations of yield curves and yield levels would be difficult. Consequently, a MOTTO is structured so that an in-the-money option at the expiration date can be settled by the exchange of the two underlying securities.
A compound option or split-fee option is an option to purchase an option. We can explain the elements of a compound option by using a long call option on a long put option. This compound option gives the buyer of the option the right but not the obligation to require the writer of the compound option to sell the buyer a put option. The compound option would specify the following terms:
The day on which the buyer of the compound option has the choice of either requiring the writer of the option to sell the buyer a put option or allowing the option to expire. This date is called the extension date.
The strike price and the expiration date of the put option that the buyer acquires from the writer. The expiration date of the put option is called the notification date.
The payment that the buyer makes to acquire the compound option is called the front fee. If the buyer exercises the call option in order to acquire the put option, a second payment is made to the writer of the option. That payment is called the back fee. An option that allows the option buyer to purchase a put option is called a caput. A Cacall grants the option buyer the right to purchase a call option.
Compound options are most commonly used by mortgage originators to hedge pipeline risk. They can also be used in any situation when a manager needs additional time to gather information about the need to purchase an option.
An important option combination in debt markets is the cap and floor, which are used to control interest rate risk exposure. Caps and floors are combinations of the same types of options (calls or puts) with identical strike prices but arranged to run over a range of time periods. The main instruments used to control interest-rate risk, including short-dated interest-rate futures and forward-rate agreements (FRAs). For example, a corporation that desires to protect against a rise in future borrowing costs could buy FRAs or sell futures. These instruments allow the user to lock in the forward interest rate available today. However, such positions do not allow the hedger to gain if market rates actually move as feared/anticipated. Hedging with FRAs or futures can prevent loss but at the expense of any extra gain. To overcome this, the hedger might choose to construct the hedge using options. For interest rate hedges, primary instruments are the cap and floor. (The terms "cap" and "floor" are not to be confused with floating-rate note products that have caps and/or floors that restrict how much a floater's coupon rate can float.)
Caps and floors are agreements between two parties whereby one party, for an up-front fee, agrees to compensate the other if a designated interest rate (called the reference rate) is different from a predetermined level. The party that benefits if the reference rate differs from a predetermined level is called the buyer, and the party that must potentially make payments is called the seller. The predetermined interest rate level is called the strike rate. An interest rate cap specifies that the seller agrees to pay the buyer if the reference rate exceeds the strike rate. An interest rate floor specifies that the seller agrees to pay the buyer if the reference rate is below the strike rate.
The terms of an interest rate agreement include (1) the reference rate, (2) the strike rate that sets the cap or floor, (3) the length of the agreement, (4) the frequency of reset, and (5) the notional amount (which determines the size of the payments). If a cap or a floor is in-the-money on the reset date, the payment by the seller is typically made in arrears.
Some commercial banks and investment banks now write options on interest rate caps and floors for customers. Options on caps are called captions. Options on floors are called flotions.
A cap is essentially a strip of options. A borrower with an existing interest-rate liability can protect against a rise in interest rates by purchasing a cap. If rates rise above the cap, the borrower will be compensated by the cap payout. Conversely, if rates fall the borrower gains from lower funding costs and the only expense is the upfront premium paid to purchase the cap. The payoff for the cap buyer at a reset date if the value of the reference rate exceeds the cap rate on that date is as follows:
| Notional amount × (Value of the reference rate — Cap rate)× (Number of days in settlement period/Number of days in year) |
Naturally, if the reference rate is below the cap rate, the payoff is zero.
A cap is composed of a series of individual options or caplets. The price of a cap is obtained by pricing each of the caplets individually. Each caplet has a strike interest rate that is the rate of the cap. For example, a borrower might purchase a 3% cap (London Interbank Offered Rate [LIBOR] reference rate), which means that if rates rise above 3%, the cap will pay out the difference between the cap rate and the actual LIBOR. A one-year cap might be composed of a strip of three individual caplets, each providing protection for successive three-month periods. The first three-month period in the one-year term is usually not covered, because the interest rate for that period, as it begins immediately, will be known already. A caplet runs over two periods—the exposure period and the protection period. The exposure period runs from the date the cap is purchased to the interest reset date for the next borrowing period. At this point, the protection period begins and runs to the expiration of the caplet. The protection period is usually three months, six months, or one year, and will be set to the interest rate reset liability that the borrower wishes to hedge. Therefore, the protection period is usually identical for all the caplets in a cap.
It is possible to protect against a drop in interest rates by purchasing a floor. This is exactly opposite of a cap in that a floor pay outs when the reference rate falls below the strike rate. This would be used by an institution that wished to protect against a fall in income caused by a fall in interest rate—for example, a commercial bank with a large proportion of floating-rate assets. For the floor buyer, the payoff at a reset date is as follows if the value of the reference rate at the reset date is less than the floor rate:
| Notional amount × (Floor rate — Value of the reference rate)× (Number of days in settlement period/Number of days in a year) |
The floor's payoff is zero if the reference rate is higher than the floor rate.
The combination of a cap and a floor creates a collar, which is a corridor that fixes interest payment or receipt levels. A collar is sometimes advantageous for borrowers because it is a lower cost than a straight cap. A collar protects against a rise in rates and provides some gain if there is a fall down to the floor rate. The cheapest structure is a collar with a narrow spread between cap and floor rates.
In an interest rate cap and floor, the buyer pays an up-front 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. 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.
The question is what type of package of options is a cap and a floor. It depends 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:
Interest rates increase → fixed income instrument's price decreases → call option value decreases and
Interest rates decrease → fixed income instrument's price increases → call option value increases
For a put option on a fixed income instrument:
Interest rates increase → fixed income instrument's price decreases → put option value increases and
Interest rates decrease → fixed income instrument's price increases → put option value decreases
To summarize:
When Interest Rates Increase | When Interest Rates Decrease | |
|---|---|---|
Value of long call | Decreases | Increases |
Value of short call | Increases | Decreases |
Value of long put | Increases | Decreases |
Value of short put | Decreases | Increases |
For a cap and floor, the situation is as follows:
When Interest Rates Increase | When Interest Rates Decrease | |
|---|---|---|
Value of short cap | Decreases | Increases |
Value of long cap | Increases | Decreases |
Value of short floor | Increases | Decreases |
Value of long floor | Decreases | Increases |
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. In contrast, if the underlying is viewed as an option on an interest rate, then buying a cap (long cap) is equivalent to buying a package of calls on interest rates. Buying a floor (long floor) is equivalent to buying a package of puts on interest rates.
An option is a contract in which the writer of the option grants the buyer 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 on a specified date). The option buyer pays the option writer (seller) a fee, called the option price. A call option allows the option buyer to purchase the underlying from the option writer at the strike price; a put option allows the option buyer to sell the underlying to the option writer at the strike price.
Interest rate options include options on fixed income securities and options on interest rate futures contracts, called futures options. There are exchange-traded options and OTC options. The actively traded exchange-traded options are futures options. OTC interest rate options are customized by dealers for their clients in terms of the expiration date, the underlying, and the type of exercise. An OTC option can be created in which the buyer may exercise prior to the expiration date but only on designated dates (so-called modified American or Atlantic or Bermuda options). An OTC option can be created whereby the buyer pays the premium at the expiration date.
There are OTC options on specific securities. There are OTC options on the spread between two yields. Spread options can be structured with a payoff that is either cash settled or requires an exchange of ownership of the two securities underlying the option. Two common spread options are options on the yield curve and options on the spread between mortgages and Treasuries.
A compound option (also called a split-fee option) is an option to purchase an option. The front fee for a compound option is the initial payment that the buyer makes. The back fee for a compound option is the fee paid by the buyer if the option is exercised.
An interest rate cap is an agreement whereby the seller agrees to pay the buyer if the reference rate exceeds the strike rate. An interest rate floor is an agreement whereby the seller agrees to pay the buyer if the reference rate is below the strike rate. The terms of a cap and floor set forth the reference rate, the strike rate, the length of the agreement, the frequency of reset, and the notional principal amount. An interest rate collar can be created by combining an interest rate cap and an interest rate floor. In an interest rate cap and floor, the buyer pays an up-front fee, which represents the maximum amount that the buyer can lose and the maximum amount that the seller of the agreement can gain.
Buying a cap is equivalent to buying a package of puts on a fixed income security, and buying a floor is equivalent to buying a package of calls on a fixed income security.
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