Interest Rate Options

An interest-rate option (IRO) gives the buyer the right to receive a cash payment if the market interest rate of a reference rate, such as the Fed Funds Rate, Secured Overnight Financing Rate (SOFR), or the prime rate, specified in the contract, is higher or lower, depending on the option, than the strike rate of the option. The payment amount is the difference between the market rate on the settlement date and the strike rate multiplied by the notional principal, specified in the option contract. Banks are the main sellers of interest-rate options. Clients are mostly corporations who need to borrow eventually, 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 affecting other options:

A call, sometimes called a borrowers' option, increases in value as interest rates rise; a put, sometimes called 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 called 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 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 interest rates vary much less than equities or other types of options. The strike of most options are referred to as strike prices, but the strike of interest-rate options are often called 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 profit from 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 + 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 called a caplet, while a single contract in a floor is a floorlet. Interest rate caps are sometimes called interest-rate calls because they go into the money if interest rates rise above the strike rate; likewise, interest-rate floors are sometimes called 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 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:

Then:

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

If the reference 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 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 be set below market rates to save on premiums. For collars, where interest rate caps are bought and floors are sold to finance the caps, strike rates can be selected to establish a zero-cost collar.

Interest-rate collars are often bought as a package from an option dealer. If the reference rate exceeds 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 on that same notional principal. If the floating rate exceeds 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 beneficial 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 exercise a caplet or floorlet on each expiration date of a cap or floor.