CDS/Bond Basis Trading
If we wish to trade bonds against CDSs or vice versa (basis trading), or calculate VaR for a portfolio, then we need to understand how the (z-)spread on a bond relates to the CDS premium, and how a change in one relates to a change in the other. The default and recovery model has been developed with a single hazard rate driver for one entity. In this chapter we look both at the practical aspects of the basis, the factors driving the basis, and how the default and recovery model can be enhanced to model bonds and CDSs more realistically.
We define the ‘basis’ as the CDS premium expressed in basis points less the bond z-spread (for a specific bond and identical maturity CDS) (see 11.3 below). Basis is bond and maturity specific.
We saw in Chapter 9 that if a bond that
a. has a single maturity (a bullet bond) (see 11.5)
b. is an FRN
c. is not, and never will be, special on repo at any date in the future (see 11.2 and 11.9)
d. is priced at par (see 11.4)
and is hedged by a CDS that
(e) has the same maturity as the bond
(f) is triggered by exactly the same events that trigger default on the bond (see section 11.8)
(g) has only that bond as the deliverable instrument (see section 11.6)
(h) pays par plus accrued on that bond if a credit event occurs (see section 11.7)
then we can set up an arbitrage trade implying that the basis is zero. We see below that ...

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