This paper provides a methodology for valuing credit default swaps when the payoff is contingent on default by a single reference entity and there is no counterparty default risk. The paper tests the sensitivity of credit default swap valuations to assumptions about the expected recovery rate. It also tests whether approximate no-arbitrage arguments give accurate valuations and provides an example of the application of the methodology to real data. In a companion paper entitled Valuing Credit Default Swaps II: Modeling Default Correlation, the analysis is extended to cover situations where the payoff is contingent on default by multiple reference entities and situations where there is counterparty default risk.
Credit default swaps have become increasingly popular in recent years. Their purpose is to allow credit risks to be traded and managed in much the same way as market risks. In 1998, trading in credit default swaps was facilitated by standard documentation produced by the International Swaps and Derivatives Association.
A credit default swap (CDS) is a contract that provides insurance against the risk of a default by particular company. The company is known as the reference entity and a default by the company is known as a credit event. The buyer of the insurance obtains the right to sell a particular bond issued by the company for its par value when a credit event occurs. The bond is known as the reference obligation and the total par value of the bond that can be sold is known as the swap’s notional principal.
The buyer of the CDS makes periodic payments to the seller until the end of the life of the CDS or until a credit event occurs. A credit event usually requires a final accrual payment by the buyer. The swap is then settled by either physical delivery or in cash. If the terms of the swap require physical delivery, the swap buyer delivers the bonds to the seller in exchange for their par value. When there is cash settlement, the calculation agent polls dealers to determine the mid-market price, Q, of the reference obligation some specified number of days after the credit event. The cash settlement is then (100 ? Q)% of the notional principal.
An example may help to illustrate how a typical deal is structured. Suppose that two parties enter into a five-year credit default swap on March 1, 2000. Assume that the notional principal is $100 million and the buyer agrees to pay 90 basis points annually for protection against default by the reference entity. If the reference entity does not default (that is, there is no credit event), the buyer receives no payoff and pays $900,000 on March 1 of each of the years 2001, 2002, 2003, 2004, and 2005. If there is a credit event a substantial payoff is likely. Suppose that the buyer notifies the seller of a credit event on September 1, 2003 (half way through the fourth year). If the contract specifies physical settlement, the buyer has the right to sell $100 million par value of the reference obligation for $100 million. If the contract requires cash settlement, the calculation agent would poll dealers to determine the mid-market value of the reference obligation a predesignated number of days after the credit event. If the value of the reference obligation proved to be $35 per $100 of par value, the cash payoff would be $65 million. In the case of either physical or cash settlement, the buyer would be required to pay to the seller the amount of the annual payment accrued between March 1, 2003 and September 1, 2003 (approximately $450,000), but no further payments would be required.
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Valuing Credit Default Swaps I: No Counterparty Default Risk
