Credit default swaps curve

This last equation shows the direct relationship between the probability of default and the market credit default swap quotes. Therefore, using equation (21.14) and the term structure of credit, we may be able to boot-strap the market implied probability of default from the credit curves, which are in effect the range of credit default swap quotes by maturity. Equation (21.14) is only approximate because in practice we would need to ensure that the timing of projected cash flows are accurately reflected in the pricing model. For example, the actual payment on the contingent leg may depend on the settlement date for the swap. 

The credit curves (or default swap curves) reflect the term structure of spreads by maturity (or tenor) in the credit default swap markets. The shape of the credit curves are influenced by the demand and supply for credit protection in the credit default swaps market and reflect the credit quality of the reference entities (both specific and systematic risk). The changing levels of credit curves provide traders and arbitragers with the opportunity to measure relative value and establish credit positions. 

In this way, any changes of shape and perceptions of the premium for CDS protection are reflected in the spreads observed in the market. In periods of extreme price volatility, as seen in the middle of 2002, the curves may invert to reflect the fact that the cost of protection for shorter-dated protection trades at wider levels than the longer-dated protection. This is consistent with the pricing theory for credit default swaps. 

A Z-spread can be calculated relative to any benchmark spot rate curve in the same manner. The question arises what does the Z-spread mean when the benchmark is not the euro benchmark spot rate curve (i.e., default-free spot rate curve) This is especially true in Europe where swaps curves are commonly used as a benchmark for pricing. When the government spot rate curve is the benchmark, we indicated that the Z-spread for nongovernment issues captured credit risk, liquidity risk, and any option risks. When the benchmark is the spot rate curve for the issuer, for example, the Z-spread reflects the spread attributable to the issue s liquidity risk and any option risks. Accordingly, when a Z-spread is cited, it must be cited relative to some benchmark spot rate curve. This is essential because it indicates the credit and sector risks that are being considered when the Z-spread is calculated. Vendors of analytical systems such Bloomberg commonly allow the user to select a benchmark. 

Another indicator of credit risk is the credit risk premium the spread between the yields on corporate bonds and those of government bonds in the same currency. This spread is the compensation required by investors for holding bonds that are not default-free. The size of the credit premium changes with the market s perception of the financial health of individual companies and sectors and of the economy in general. The variability of the premium is illustrated in FIGURES 10.2 and 10.3 on the following page, which show the spreads between the U.S.-dollar-swap and Treasury yield curves in, respectively, February 2001 and February 2004. 

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