The swap terms available to the insurance company are as follows:
- Every six months the life insurance company will pay LIBOR.
- Every six months the life insurance company will receive 8.40%.
What has this interest-rate contract done for the bank and the life insurance company? Consider first the bank. For every six-month period for the life of the swap agreement, the interest-rate spread will be as follows: Read the rest of this entry »
So far we have merely described an interest-rate swap and looked at its characteristics. Here we illustrate how they can be used in asset/liability management. Other types of interest-rate swaps have been developed that go beyond the generic or “plain vanilla” swap described and we describe these later.
An interest-rate swap can be used to alter the cash flow characteristics of an institution’s assets so as to provide a better match between assets and liabilities. The two institutions we use for illustration are a commercial bank and a life insurance company. Read the rest of this entry »
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 »
