Research & Publications
Back-to-Basics

The following article is reprinted from the May/June, 2000 issue of
On the Edge, the Interactive Data Fixed Income Analytics bimonthly newsletter.

Back-to-Basics: Interest Rate Caps & Floors

Teri Geske
Senior Vice President, Product Development


The next release of BondEdge, version 4.2, includes a new model for Interest Rate Caps & Floors (see related article on page 5). Many of our clients are now using these derivatives for interest rate risk management, so we thought it would be useful to review the fundamentals of caps and floors in this Back-to-Basics article.

Caps and floors can be thought of as an insurance policy against a rise or decline in interest rates. They can be used in asset/liability management to adjust cash flows on either side of the balance sheet, and can be used to manage the convexity of a portfolio (more about this later). The buyer of an interest rate cap is purchasing protection against an increase in a referenced interest rate, usually 3 month LIBOR or perhaps some constant-maturity Treasury (CMT) rate. If the referenced rate rises above a certain level, called the “strike” rate, the cap buyer receives a payment equal to the difference between that interest rate and the strike rate, based on a notional amount of principal (note that in a standard transaction, the strike rate is set between the cap buyer and the cap seller at the outset of the contract, although there are more exotic types of caps and floors where the strike rate can change during the life of the contract). A floor is the opposite of a cap; the buyer is protected against a decline in rates below the strike rate. A collar is a combination of a cap and floor; if you are “long” the collar, you have purchased the cap and sold the floor. This is appropriate for a portfolio or balance sheet that would be hurt by a rise in rates but is not particularly at risk in a falling rate environment. A collar is a popular instrument as it essentially lowers the cost of purchasing the cap alone. If the cap and floor have the same price, the cost of the collar is zero. This is termed a “no-cost” or “zero-cost” collar, and can be deliberately created by finding the strike rate that will cause the value of the floor to be equal to that of the cap.

Consider this example, where a floor is used to protect earnings: a bank has a portfolio of $100 million in floating rate loans that earn, on average, 3 month LIBOR + 1.00%. The bank has determined that if the income from the portfolio drops below 6.00%, their earnings will be unacceptably low. Since LIBOR is now at about 6.25% the portfolio is currently earning 7.25%, well above the 6.00% required minimum; however, the banks wants to protect itself against a decline in rates of 125bps or more. A floor on 3 month LIBOR with a strike of 5.0% on a notional amount of $100mm would provide this protection. If, on any of the quarterly “reset” dates during the life of the contract (caps typically have quarterly or semi-annually resets), LIBOR is less than 5.0%, the bank will receive a payment at the end of the quarter equal to (5.0% - 3mo LIBOR)/4 X $100mm. This payment would effectively increase the bank’s income from the portfolio back up to 6.00%, even though the average loan rate of LIBOR + 1% had fallen below 6.0%. Of course, the bank must pay an upfront premium for this protection and if 3 month LIBOR remains above 5.0% for the life of the contract, the bank receives no payments.

This payoff profile is exactly like that of an insurance policy, say car insurance, where the policy-holder receives no payment for the term of the policy unless the car is in a wreck. As with car insurance, the buyer of a cap or floor pays a premium for protection against a rise/fall in interest rates for a specified period of time, typically ranging from 1 to 5 years, but often as long as ten years. Just as the cost of car insurance is a function of the current value of the car, the amount for which it is insured, the term of the policy and the likelihood of getting into a wreck, we can intuitively see that the price or premium paid for a cap or floor is a function of the current level of rates, the strike rate on the cap/(floor), the term of the contract and the likelihood that interest rates will exceed the strike rate of a cap (or drop below the strike rate of a floor) during the life of the contract. The likelihood that rates will move higher or lower is, of course, determined by the assumed volatility of interest rates into the future. Now, if we recall that volatility is a key determinant of an option’s value1, we can understand that caps and floors are, in fact, options on interest rates. In fact, caps and floors are actually a series of options whose individual expiration dates correspond to the reset dates of the cap/floor contract (e.g., a 5 year cap with quarterly resets is a series of 20 quarterly option contracts). Each of these individual contracts is referred to as a “caplet” (or “floorlet”). The value of each individual caplet/(floorlet) depends on the volatility of interest rates corresponding to that particular date, and the sum of the value of the caplets gives us the price of the cap. As with all options, the higher the volatility, the greater the value (price) of a cap or floor. Therefore, the volatility one uses to value a cap/floor is a key variable in pricing these instruments, and the price of a cap or floor implicitly assumes some volatility rate. These “implied volatility” rates derived from cap prices provide useful information about the market’s consensus expectations for future interest rate volatility.

In the cap market, traders speak of implied volatilities that are derived by inputting a cap price into the Black ‘76 option model (of the Black-Scholes-Merton family of models). Using the Black model for this purpose allows all market participants to speak the same language - in other words, if one trader says “the 3 year cap volatility is 14%,” it is understood to be a volatility derived from the Black ‘76 model. Therefore, we can input a price to obtain a Black volatility and vice versa. There is a different implied Black volatility for caps of each maturity - a one year cap volatility, two year volatility, and so on. This allows us to derive an implied “term structure of volatility” from the cap market.

We noted earlier that interest rate caps/floors can be used to change the convexity of a portfolio. This is due to the fact that these instruments are, in fact, options. We know that embedded options greatly affect the convexity of bonds - a non-callable bond of intermediate maturity has modest, positive convexity (approximately 0.10 for a 5 year maturity bond), whereas an at-the-money callable bond has substantial negative convexity, because the bond investor is short the call option. So, the difference between the small, positive convexity of a non-callable bond and the large, negative convexity of a callable bond is due to the convexity of the embedded call option. Since we noted above that an interest rate cap is really a series of call options, we can see that the convexity of a portfolio can be increased by buying an interest rate cap.

There are many more details about valuing and using caps and floors that are beyond the scope of this article but we hope this has been a useful review of the basics. If you have any suggestions for future Back-to-Basics topics, please contact marketing at (310) 479-9715 or via email at fia.marketing@interactivedata.com


1See Back-to-Basics article, “Volatility and Option Valuation,” August 1996 - on this web site under "Back-to-Basics."