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I have not understood which "zerorati" I must use for the bootstrap of the PD from the curve of the CDS spreads. Can you help me please? I consulted O'Kane (2008) and Brigo and Mercurio (2006), but I'm not sure of the choice.

https://it.mathworks.com/help/finance/bootstrapping-a-default-probability-curve.html

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This is, indeed a delicate matter. You might want to use zeros bootstrapped from the relevant OIS curve used for collateral remuneration. So you might want to use EONIA (€STR) swaps for EUR, SONIA for GBP and so on.

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  • $\begingroup$ Thanks a lot for your answer. If I have understood, when I have at the time "t" the CDS spreads quotation for all tenors (1y,2y,...,30y), I have to consider the "zero retes" at the time "t" a curve of the (for example) of EONIA Swaps (because my analysis starts ex-ante October 2019) for the same tenors (1y,2y,...,30y)? Do these exist? $\endgroup$
    – d0whes
    Commented Mar 28, 2020 at 10:52
  • $\begingroup$ On your observation date, you collect CDS and OIS swap rates. From those OIS quotes you bootstrap zero rates, which you then use in your CDS formula. $\endgroup$
    – Kermittfrog
    Commented Mar 28, 2020 at 13:39
  • $\begingroup$ You should use Libor rates, or more accurately, OIS rates. If you are willing to consider using Python and FinancePy then this is an example which should make clear what to do github.com/domokane/FinancePy/blob/master/notebooks/products/… $\endgroup$
    – Dom
    Commented Dec 23, 2020 at 2:07

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