Can Bond Spreads Be Bootstrapped Like CDS Spreads?

Summary

The document poses a fixed-income modeling question: whether a bond spread curve can be converted into a credit curve by applying the same bootstrapping function used for a CDS par-spread curve. The setup assumes a standard CDS framework with piecewise constant forward or hazard rates. The bond spreads in question are yield-to-maturity spreads on risky fixed-coupon bonds, measured over swap rates at matching maturities; the bonds need not trade at par.

The central issue is whether these two kinds of spread carry interchangeable information about default risk. The document provides no answer, supporting analysis, or empirical evidence, so it does not establish that applying CDS bootstrapping to bond spreads is valid. It also leaves unresolved how differences in instrument structure and spread calculation might affect the resulting credit curve. Readers should treat this as an open modeling question rather than a demonstrated method.

Key ideas

• The question compares CDS par spreads with risky bond yield spreads over swap rates.
• The proposed method applies a CDS spread bootstrapping function to the bond spread curve.
• The framework described assumes piecewise constant forward or hazard rates.
• The document does not answer whether bond and CDS spreads are interchangeable.

Tags

# Bootstrapping bond spreads as in the standard CDS model


# Bootstrapping bond spreads as in the standard CDS model












Suppose that we have a spread curve $\boldsymbol{s}:=(s_1, ..., s_n)$, where $s_i$ are CDS par spreads. Moreover, assume the standard ISDA model framework, i.e. piecewise constant forward / hazard rates. Let $g$ be the function such that $\boldsymbol{c} = g({\bf s})$, where $\boldsymbol{c}:=(pd_1,...,pd_n)$ is the credit curve corresponding to $\boldsymbol{s}$. Thus, applying $g$ is equivalent to bootstrapping a CDS spread curve.

Now, let there also be a bond spread curve $\boldsymbol{bs}:=(bs_1, ..., bs_n)$. Here, $bs_i$ is computed as the spread of YTM (yield-to-maturity) of a risky fixed-coupon bond (not necessarily trading at par) over the LIBOR swap rate for the maturity horizon. Finally, the question: is it plausible to construct the credit curve $\boldsymbol{bc}$ corresponding to $\boldsymbol{bs}$ using the very same (CDS bootstrapping) function $g$, i.e. as $\boldsymbol{bc} = g({\bf \boldsymbol{bs}})$? That is, to which extend are the CDS and bond spreads interchangeable?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.