If the var-covar matrix for equities takes the return on equity prices, what should the var-covar matrix for credit derivatives (like a CDS) take?

Should it be the probability of default, since that usually determines the prices of the credit derivatives?

I'm not sure on what would be the equivalent of equity return for credit derivatives and would appreciate any help on this.


1 Answer 1


As a general principle, you should try to calculate statistics from market observables. Credit spreads are observable. If CDS trades, then you can see CDS quotes. If debt trades or is marked to market, then you can figure out how much they yield in excess of credit risk-fgree rates. But probabilities of default (physical or risk-neutral) are not observable.

  • $\begingroup$ So, if I use excess of bond yield over the risk free rate to compute the covar matrix, would that be fine? $\endgroup$ Mar 4, 2022 at 13:00
  • 1
    $\begingroup$ Yes. In a simplest case, use one spread per ossuer. Or have term structure of the spread (may or may not be useful). If an issuer's debt in multiple currencies, you can have spreads by currencies (not much difference). You can split the spread into country of risk + rating + idiosyncratic issuer. $\endgroup$ Mar 4, 2022 at 16:56

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