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 »
A total return swap in the fixed-income market is a swap in which one party makes periodic floating-rate payments to a counterparty in exchange for the total return realized on a reference obligation or a basket of reference obligations. A total return payment includes all cash flows that flow from the reference obligations as well as the capital appreciation or depreciation of those reference obligations. When the reference obligation is a bond market index, the swap is referred to as a total return index swap.
The party that agrees to make the floating payments and receive the total return is referred to as the total return receiver; the party that agrees to receive the floating payments and pay the total return is referred to as the total return payer.
Notice that in a total return swap, the total return receiver is exposed to both credit risk and interest-rate risk. For example, the credit risk spread can decline (resulting in a favorable price movement for the reference obligation), but this gain can be offset by a rise in the level of interest rates. Read the rest of this entry »
