hard · FRM Part 2 Credit Risk
A CDO tranche desk uses the Gaussian copula with a single correlation parameter to map a CDS index to tranche prices. Empirically the desk observes a 'correlation smile': calibrating each tranche separately to its market price yields a higher implied correlation for the equity (0–3%) and senior tranches than for the mezzanine tranches. A risk manager must explain why a single base correlation surface (rather than compound/implied correlation) is preferred for interpolating bespoke tranches.
What is the strongest technically correct justification?
- Base correlation is preferred because compound correlation can be non-monotonic and non-unique for mezzanine tranches, whereas base correlation parametrizes a sequence of equity tranches that is monotone in detachment and admits unique calibration and arbitrage-free interpolation
- Base correlation is preferred because it directly fits the physical-measure default correlation observed in historical data, removing the need for a risk-neutral copula entirely
- Compound correlation is rejected because it always overstates senior-tranche correlation, systematically mispricing the index relative to the sum of tranches
- Base correlation is preferred because it makes the copula correlation constant across the capital structure, eliminating the smile and restoring a single-factor model
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