Funds Investing

Valuing Caps and Floors

The arbitrage-free binomial model can be used to value a cap and a floor. This is because, as previously explained, 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 all the caplets are then summed. The same can be done for a floor.

To illustrate how this is done, we will once again use the binomial interest-rate tree to value an interest rate option. Consider first a 5.2%, three-year cap with a notional amount of $10 million. The reference rate is the one-year rates in the binomial tree. The payoff for the cap is annual.

Exhibit 25-12 shows how this cap is valued by valuing the three caplets. The value for the caplet for any year, say year X, is found as follows. First, calculate the payoff in year X at each node as either zero if the one-year rate at the node is less than or equal to 5.2%, or the notional principal amount of $10 million times the difference between the one-year rate at the node and 5.2% if the one-year rate at the node is greater than 5.2%

Then, the backward induction method is used to determine the value of the year X caplet. Read the rest of this entry »

An interest-rate agreement is an agreement between two parties whereby one party, for an upfront premium, agrees to compensate the other at specific time periods if a designated interest rate, called the reference rate, is different from a predetermined level. When one party agrees to pay the other when the reference rate exceeds a predetermined level, the agreement is referred to as an interest-rate cap or ceiling. The agreement is referred to as an interest-rate floor when one party agrees to pay the other when the reference rate falls below a predetermined level. The predetermined interest-rate level is called the strike rate.

The terms of an interest-rate agreement include

1. The reference rate
2. The strike rate that sets the ceiling or floor
3. The length of the agreement
4. The frequency of settlement
5. The notional principal amount

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