# Interest Rate Options

An **interest-rate option** (IRO) gives the buyer the right to receive a cash payment if market interest rate of a reference rate, usually the libor, specified in the contract, is higher or lower, depending on the option, than the strike rate of the option. The amount of the payment will be based on the difference between the market rate on the settlement date and the strike rate multiplied by the notional principal, specified in the option contract, to calculate the total payment. Banks are the main sellers of interest-rate options. Clients are mostly corporations who need to borrow at some point in the future, so they want to ensure against adverse changes in interest rates during the interim. Because IROs are settled in cash, the client does not need to borrow from the bank that sold it the IRO; if the IRO is in the money and the client exercises the option, then the bank pays the cash settlement to the client. IROs have no secondary market, but if the client wishes to terminate the option before expiration, then the IRO can be sold back to the bank for residual or fair market value.

IRO premiums are determined by the same factors that affect other options:

- current market rate of the underlying
- strike price or rate
- time until expiration
- market volatility, and
- whether it is a call or put.

A **call**, sometimes referred to as a **borrowers' option**, increases in value as interest rates rise; a **put**, sometimes referred to as a **lenders' option**, increases in value if interest rates fall. The **expiry date** is when the option can be exercised, which is 2 days before the **settlement date**, sometimes known as the **value date**, unless the currency is sterling, in which case the option is exercised on the settlement date.

Interest-rate options differ from equity options in that they generally cover an extended duration rather than a single date. Furthermore, because interest rates have a major effect on the economy, central banks prevent interest rates from reaching extremes, so the variation of interest rates is much less than what could possibly occur with equities or other types of options. The strike of most options are referred to a strike prices, but the strike of interest-rate options are often referred to as **strike rates**, since these options go into the money if the interest rate rises above or below the strike rate, depending on the option type.

The advantage of IROs over interest rate futures and forward rate agreements, like other options, is that the holder has the right, but not the obligation, to exercise the option. Therefore, if an IRO holder has a cap, but interest rates subsequently decline, then the holder can simply let the option expire and take advantage of the lower interest rates.

When an IRO is exercised, the IRO seller pays the IRO buyer the difference between the strike rate and the market rate, which creates an effective interest rate equal to the strike rate plus the option premium.

## Caps, Floors, and Collars

Caps, floors, and collars are over-the-counter (OTC) options used extensively to hedge interest-rate risks. Usually, 1 of the counterparties is a bank. An **interest-rate cap** sets a maximum interest rate, an **interest-rate floor** sets a minimum interest rate, and an **interest-rate collar** sets both a maximum and minimum interest rate by combining a cap and a floor. These IROs usually consist of strips of options of the same type and usually at the same strike rate, covering a series of successive periods. One of these contracts in a cap is referred to as a **caplet**, while a single contract in a floor is referred to as a **floorlet**. Interest rate caps are sometimes referred to as **interest-rate calls** because they go into the money if interest rates rise above the strike rate; likewise, interest-rate floors are sometimes referred to as **interest-rate puts** because they go into the money when interest rates decline below the strike rate.

Collars are established by buying a cap and selling a floor at a lower interest rate. The collar is a type of spread where one option is partly or wholly financed by selling another option. Most interest-rate collars consist of a long cap and a short floor. The income from selling the floor is used to offset, wholly or in part, the cost of the cap. However, if the referenced interest rate drops below the floor, then the collar will lose money proportionate to the amount that the referenced interest rate drops below the floor rate.

The premiums for interest-rate options are generally expressed as basis points per notional principal, where 100 basis points = 1%. So if a hedger wanted to buy an option for 150 basis points on $1 million, then the actual cost would be $1 million × 1.5% = $15,000.

### Example: Calculating the Price of a Caplet

If:

- notional principal = $100 million
- strike rate = 5% per annum
- contract period = 6-month term
- expiration: 6 months after purchase
- premium rate = 0.25% per annum

Then:

- Caplet Premium = $100 million × 0.25%/2 = $125,000

If, at the expiration of the European option, the US dollar libor rate is 6%, then this must be paid:

- Settlement Sum = $100 Million × (6% – 5%)/2 = $500,000

If the libor rate were 4% instead of 6%, then the option holder would simply let the option expire.

An interest-rate cap is simply a series, or **strip**, of caplets covering successive periods. The caplets are priced according to expected future interest rates, so buyers will generally set the strike rates higher than current interest rates to save on the premium, in much the same way that the buyer of a stock option will buy an option with a strike price higher than the current stock price to pay a lower premium. Likewise, the strike rate of a floor will generally be set below current market rates to save on premiums. For collars, where interest rate caps are bought and floors are sold to finance the caps, strike rate can be selected so that a **zero-cost collar** can be established.

Interest-rate collars are generally bought as a package from an option dealer. If the reference rate is above the cap rate, then the dealer pays the buyer the net difference between interest rates; if the reference rate is below the floor, then the buyer must pay the dealer the difference between the floor rate and the market rate at expiration multiplied by the notional principal; if the reference rate falls between the floor and the cap, then no payment is made by either party.

An interest-rate swap is a contract in which the buyer of the swap agrees to a fixed rate of interest on a notional principal while the seller agrees to a floating rate, such as the libor, on that same notional principal. If a floating rate is higher than the fixed-rate, then the seller pays the buyer; if lower, then the buyer pays the seller. A **payer swaption** is a European-style option that grants the holder the right to enter into a swaption. If the holder decides to enter into the swaption, then the interest rates are fixed for the contract period, and the buyer may have to pay the seller the difference in interest rates if the floating rate is less than the fixed rate. Thus, a swaption is less advantageous than a cap, a floor, or a collar, since the decision to exercise or not can only be made once for a payer swaption, but can be made on the expiration date of each cap or floor. Thus, the buyer can decide to exercise a caplet or floorlet on each expiration date of a cap or floor.

## Eurodollar Options

Eurodollar options give the holder the right to enter into a Eurodollar futures contract. Eurodollars futures prices are based on the anticipated US dollar (USD) libor interest-rate offered during the contract period on Eurodollar deposits — USD-denominated deposits held in banks outside of the United States. Eurodollar options can also be used to construct caps and floors. The **Chicago Mercantile Exchange** (**CME**) sells these American-style options based on a 3-month term that begins on a future date. The payment is calculated using a $1 million notional principal. A 1% change in the futures price equals a 1 basis point change in the interest rate for the contract period. CME offers both calls and puts. A **call** gives the holder the right to enter into a Eurodollars futures contract, which benefits from falling interest rates. A **put** gives the holder the right to sell a Eurodollar futures contract, which profits from rising interest rates. The premium is expressed as basis points multiplied by the minimum tick value of $25.

The strike rate of the futures contract is generally set as the interest rate subtracted from 100, so a futures contract with a strike rate of 3% would be equal to 97, since 100 – 97 = 3. So if a call has a strike price 96, and the interest rate falls to 1%, which is equal to 99 for the futures contract, then the call buyer can exercise the option to earn 300 basis points × $25 = $7500. A put with the same strike price would simply expire worthless.

CME also offers **mid-curve options**, which are options on Eurodollar futures contracts covering 1, 2, and 5-year contracts. The reference rate for a mid-curve option is not a spot rate but a forward rate based on the value of a Eurodollar futures for the forward period. Mid-curve options, so named because they cover the middle of the yield curve, are short-dated options with terms of 1 year or less, with quarterly expirations plus the 2 front months. There are also **weekly mid-curve options** that cover the quarterly Eurodollar futures expiring one year from the nearest non-expired quarterly mid-curve. Trading on weekly options terminates on each Friday that is not an expiration day for a quarterly, serial, or mid-curve option. So, in early June, weekly contracts would have the Eurodollar futures for June of the following year as its underlying contract, while one expiring later in the month, would have the September contract for the following year, since by then, the June mid-curve would have already expired.

Mid-curve options based on the 1-year Eurodollar futures are referred to as the **red mid-curve options** and are the most liquid. Contracts based on the 2-year Eurodollar futures are referred to as the **green mid-curve options**.

## Euro and Sterling Interest-Rate Options

Other interest rates options are sold in Europe on NYSE Liffe, part of NYSE Euronext. Unlike most other options, where the full premium must be paid, the interest rate options offered by NYSE Liffe are purchased like a futures contract, in that the buyer deposits an initial margin set by the exchange. The count is managed as **variation margin**, where the account is mark-to-market daily, incremented or decremented according to the market interest rates for that day.

One such option is for the **Euribor** (**Euro Interbank Offered Rate**), which is the key reference rate for short-term euro interest rates. Like other financial futures, the Euribor option has expiration dates in March, June, September, our December plus other near months. A Euribor future contract is based on a notional principal of €1 million. A 1 basis point move is equal to €25, but the price can change by ½ tick, equal to €12.50. Options are for futures that expire in the same month that the option expires, so a March call or put allows the holder to buy or sell a futures contract that expires in March.

There is also a 3-month sterling interest-rate futures with a notional principle of 500,000 British pounds, so 1 tick = GBP 12.50.