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CHAPTER 14 - VALUATION OF INTEREST RATE ... > V. CAPS AND FLOORS
V. CAPS AND FLOORS
In applying the backward induction methodology to valuing caps and floors, the decision to exercise at a node will depend on whether or not the cap or the floor is in the money. Remember that a cap and a floor are nothing more than a package or strip of options. More specifically, they are a strip of European options on interest rates. Thus, to value a cap, the value of each period’s cap, called a caplet, is found and the values of all the caplets are then summed. The same can be done for a floor.
To illustrate how this is done, we will use the binomial tree given in Exhibit 13a. We will simplify the analysis by ignoring the difference in the timing of the payments for caps and floors. Specifically, the settlement payment for caps and floors is in arrears. Allowing for that would require complicating the presentation and revising the binomial tree.196 Consider first a 5.2% 3-year cap with a notional amount of $10 million. The reference rate is the 1-year rate in the binomial tree. The payoff for the cap is annual.