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Choosing the Discount Curve for CDS Default Probability Bootstrapping

Article Quant Q&A · Author: d0whes
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Summary

The document addresses which zero rates to use when bootstrapping a default probability curve from credit default swap spreads. The response recommends discounting with the curve relevant to collateral remuneration, typically the applicable overnight indexed swap curve. It names currency-specific examples, including EONIA or €STR for euros and SONIA for sterling.

This guidance highlights that CDS valuation depends on a discount curve consistent with the collateral convention, rather than an arbitrary set of zero rates. The document is brief and offers no derivation, numerical example, or comparison of alternative collateral arrangements. Its recommendation is therefore a starting point for curve selection; implementation still depends on the currency and the collateral terms of the CDS being valued.

Key ideas

  • CDS default probability bootstrapping requires selecting a discount curve for valuation.
  • The response recommends using the overnight curve associated with collateral remuneration.
  • The appropriate curve depends on the currency, with EONIA or €STR and SONIA given as examples.
  • The document provides brief curve-selection guidance but no derivation or worked bootstrap.

Tags

Fixed incomeDerivatives pricingStatistics
Full text
# MATLAB - Probability Default with CDS Bootstrapping


# MATLAB - Probability Default with CDS Bootstrapping












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

## Answer by Kermittfrog (score 1)

https://quant.stackexchange.com/a/51860

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