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Merton’s model, credit risk and volatility skews - page 8 / 26





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John C. Hull, Izzy Nelken and Alan D. White

and Derivatives Association produced its first version of a standardized contract in 1998.9

GFI, a broker specializing in the trading of credit derivatives, provided us with CDS quotes for the period January to December, 2002. The data contain in excess of 120,000 individual CDS quotes. Each quote contains the following information:

the date on which the quote was made; the name of the reference entity; the life of the CDS; whether the quote is a bid (wanting to buy protection) or an offer (wanting to

sell protection); and the CDS spread quote in basis points.

Each quote is a firm quote for a minimum notional of US$10 million. The refer- ence entity may be a corporation such as Blockbuster Inc., a sovereign such as Japan, or a quasi-sovereign such as the Federal Home Loan Mortgage Corporation. During the period we are considering CDS quotes are provided on 1,597 named entities: 1,500 corporations, 60 sovereigns and 37 quasi-sovereigns. Of the refer- ence entities 796 are North American, 451 are European and 330 are Asian and Australian. The remaining reference entities are African or South American.

We used only five-year quotes in our analysis (approximately 85% of the quotes in our data set were for five-year CDS). When there were both five-year bid and offer quotes on a reference entity in a day, we calculated what we will refer to as an “observation” on the five-year CDS spread as the average of the maximum bid and minimum offer.10 As shown by Duffie (1999) and Hull and White (2000), the five-year credit default swap spread is, in theory, very close to the credit spread of the yield on a five-year par yield bond issued by the reference entity over five-year par yield risk-free rate.

3.2 Implied volatility data

From the list of entities covered by the CDS data, we chose optionable US equities with current stock prices over US$20. This resulted in a list of 325 com- panies. The Bloomberg system, which has been archiving the implied volatility of options on US equities since the beginning of 2002, was polled to determine for which of the names implied volatility data were available. This reduced the

market price, x, of a bond issued by the reference entity a specified number of days after the credit event. The payment by the seller is then is 100 – x per $100 of principal.

8 The CDS spread is very close to the credit spread observed in the corporate bond market when the credit spread is measured relative to the swap rate. For more information on the rela- tion between CDS spreads and bond credit spreads, see Blanco, Brennan and Marsh (2003), Longstaff, Mithal and Neis (2003) or Hull, Predescu and White (2004).

9 A more complete description of credit default swaps and the CDS market can be found in, for example, Duffie (1999).


When there was a trade the bid equals the offer.

Journal of Credit Risk

Volume 1/Number 1, Winter 2004/05

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