Pricing Caplets and Floorlets with Excel

A Cap or Floor option protect the buyer from changes in interest rates. A cap option limits the interest rate paid by a borrower, and consist of a series of consecutive European-style call options. Each call option is called a caplet.  A caplet give the holder a payment if the interest rate on a variable rate loan is above a predetermined strike.  The payment is equal to the difference between the interest rate and the strike, and is usually made every month, three months or six months.

The payment on a LIBOR cap is given by the following equation, where the Day Basis is usually 360.

Libor Cap Payment

Caplets are often priced with the Black model.  This is a variant of the Black-Scholes model for pricing European-style options, and is used to predict forward prices.  The Black model gives the value of a caplet at maturity, with the fair market value being the net present value.  The price of the cap option is hence the sum of price of the individual caplets.

Pricing Caplets and Floorlets in ExcelThe Black model, however, assumes that short term interest rates are constant. Cap options on short-term interest rates, however, will only be of value if the interest rate is not constant.  Hence other models with stochastic interest rates have been developed.

Quantitative analysts often cover the cost of buying a cap by selling a cap with a higher strike at the same time. This is known as a corridor strategy, and protects the holder if the interest rate rises between the two strikes.  Corridor strategies are risky if short term interest rates break through the higher strike.

A floor option is an interest rate floor, and consist of a series of consecutive European style put options. With floorlets, the holder collects payments for every period the interest rate is below the predetermined strike.  Typically, lenders employ floorlets to hedge against falling interesting on loans with a variable interest rate.

Purchasing a cap and selling a floor on the same interest rate is known as a collar option. The holder pays between a minimum and maximum interest rate over lifetime of the collar. This limits liability to a predetermined range.

Cap and floor options are also used by energy traders to hedge against possible changes in fuel prices.

Download Excel Spreadsheet to Price Caplets and Floorlets


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