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Interest rates standard options are "caps" and "floors." The "cap" guarantees a maximum rate to the buyer. Borrowers are interested by caps since they set a maximum paid interest cost. A cap is an option: It has value only when the rate is above the guaranteed rate, otherwise, it is worthless. The "floor" guarantees a minimum rate to the buyer. Investors are interested by floors because they are willing to be protected against declining interest revenues. A floor is an option: It has value only when the rate is below the guaranteed rate, otherwise, it is worthless.

Payoff of Interest Rate Options

The mechanism of a cap providing a guaranteed maximum rate is as follows. The borrower has an original variable rate debt, which does not change. Assume that the borrower's debt is indexed to the Libor 3-month. The strike is 8%. If Libor 3-month is 10%, the borrower pays only the strike 8%, and the seller of cap pays the difference: 10% (spot rate) - 8% (strike) = 2%. If Libor 3-month becomes 6%, the borrower pays only 6%.

A floor provides a minimum guaranteed rate. The mechanisms are the same as above. The lender has an original variable rate debt, which does not change. Say the reference rate is Libor 3-month and that the strike is 8%. If Libor 3-month is 10%, the lender receives 10%, and the seller of cap does not pay anything. If Libor 3-month is 6%, the lender receives the strike 8% and the seller of cap pays the difference 8% (guaranteed rate) - 6% (spot rate) — 2%.


A "collar" combines a cap and a floor. The buyer of a collar buys a cap from the bank and sells a put to the bank. The premium received from the sale of the put reduces the cost of the straight cap. The buyer is typically a borrower floating rate. The borrower is protected against interest rates higher than the cap guaranteed rate, but pays at least the minimum rate guaranteed by the floor to the bank. The borrower pays the prevailing rate within the range of rates of the cap and the floor guaranteed rates, no more than the cap rate, no less that the floor rate. The primary interest of a collar is the lower net premium paid than for a straight cap, since the premium is that of cap minus that of the floor sold to the bank. Such instruments serve for minimizing the cost of the hedge, the drawback being the minimum rate to be paid if rates decline. In Figure 7.13, the holder of the collar does pay less than the floor and does not pay more than the cap.

Another view of the collar would be in payoff terms, as a function of the future spot rates. When the interest rate moves up and hits the strike of the cap, the buyer of the cap pays a fixed rate equal to strike. When the interest rates moves down to the strike of the floor, the buyer of the collar will pay again a fixed, lower rate. In between the rate varies as the market rate. (See Figure 7.14.)


FIGURE 7.13 Collar

Payoff of collar

FIGURE 7.14 Payoff of collar

Options as Volatility Instruments

Those are simple examples using simple contracts. They are generic hedges, used with instruments called "plain vanilla," because they have no exotic features embedded in them. There are various ways of combining options on interest rates. Notably, the views of traders will differ from the hedger's view. For example, the trader will see options on interest rates as volatility instruments, and could use options to bet on volatilities. Consider a simple example to illustrate this point. If a trader buys both a cap and a collar, instead of buying one and selling the other one, with the strike price of the cap higher than that of the floor, it has a long position on volatility. The position is long because the trader gains when interest rate volatility increases. The payoff graph would be as shown in Figure 7.15.

Payoff of bought cap and floor

FIGURE 7.15 Payoff of bought cap and floor

As long as the interest rate remains within the strikes, the trader has paid a premium and makes a loss. But if the interest rate moves beyond the strikes, on either side, the trader gains if the gross payoff more than compensates the premium paid (which cumulates the premium of the cap and of the floor). This combination makes up a strangle. The trader is long in the strangle, and wins when the volatility of interest rates is high enough to make either option sufficiently in-the-money. Such combinations apply as well for any underlying, and there are a variety of combinations of options, which allow having payoffs with a variety of shapes.

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