Optimal Stochastic Recovery for Base Correlation

On the back of monoline protection unwind and positive gamma hunting, spreads of the senior tranches of the CDX investment-grade index have widened so much that they went beyond the maximum spread levels that standard Gaussian Copula model can allow. Indeed, using a 40% recovery assumption and 100% default correlation gives a spread of 39bp on the 5Y [30-100] tranche while the market price was 55bp on June, 27th 2008 with a CDX.IG9 ref of 148bp.An other challenge is the emergence in the market of a new super senior tranche [60-100] that used to have no value (under the 40% recovery assumption) and that starts showing up on the screens initially at 5bp then 10bp and lately at low to mid twenties.We present in this document an enhancement to the standard copula Model by introducing an optimal stochastic recovery specification