Let’s illustrate the mechanics of a standard single-name credit default swap. Assume that the reference entity is the ABC Corporation and the reference obligation is the ABC Subordinated Debenture due 2110. The swap premium—the payment made by the protection buyer to the protection seller —is 550 basis points. If a credit event occurs, the protection seller pays the protection buyer the notional amount of the contract. In our illustration, we will assume that the notional amount is $10 million.
The notional amount is not the par value of the reference obligation. For example, suppose that a bond issue is trading at 73.53 (par value being 100). If a portfolio manager owns $13.6 million par value of the bond issue and wants to protect the current market value of $10 million (approximately equal to 73.53% of $13.6 million), then the portfolio manager will want a $10 million notional amount. If a credit event occurs, the portfolio manager will deliver the $13.6 million par value of the bond and receive a cash payment of $10 million. 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 »
In an interest-rate swap, two parties (called counterparties) agree to exchange periodic interest payments. The dollar amount of the interest payments exchanged is based on a predetermined dollar principal, which is called the notional principal amount. The dollar amount that each counterparty pays to the other is the agreed-upon periodic interest rate times the notional principal amount. The only dollars that are exchanged between the parties are the interest payments, not the notional principal amount. In the most common type of swap, one party agrees to pay the other party fixed-interest payments at designated dates for the life of the contract. This party is referred to as the fixed-rate payer. The other party, who agrees to make interest rate payments that float with some reference rate, is referred to as the floating-rate payer. The frequency with which the interest rate that the floating-rate payer must pay is called the reset frequency. Read the rest of this entry »
