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 long-run historical rating-transition and default-timing data, entirely removing the practical need to calibrate any risk-neutral copula model to market tranche quotes.
- Compound correlation is rejected because it always systematically overstates senior-tranche implied correlation relative to observed market quotes, which historically mispriced the full index tranche stack relative to the arithmetic sum of its constituent tranche prices.
- Base correlation is preferred because it forces the implied copula correlation parameter to remain exactly constant across the entire capital structure, thereby eliminating the correlation smile altogether and restoring a clean, fully tractable single-factor Gaussian copula pricing model.
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