June 29th, 2005, 9:23 am
I found that depending on the base correl model there can be some inconsistencies:you get the market distribution of losses as Prob(L > K) = d/dK D(K) where D(K) is the (undiscounted) price of the default leg of the 0-K tranche. With a base-correl model D(K) is computed as D(K) = f(K, baseCorr(K)) where f(K, rho) is the Gaussian Copula (undiscounted) price of a 0-K default leg at correlation rho, so you simply get Prob(L > K) = df/dK + d f/dbaseCorr * d baseCorr / dK (1)If the interpolation method baseCorr(K) as a function of K has discontinuous 1st derivative (that's the case with linear interpolation for instance) then the cumulative distribution function Prob(L > K) is discontinuous, which means it has some Dirachs on specific strikes! But Worse!: assume K* is such a 1st derivative discontinuity point. Then Prob(L = K*) = d f/dbaseCorr * (d baseCorr / dK (K*-) - d baseCorr / dK (K*+)), and if d baseCorr / dK (K*-) < d baseCorr / dK (K*+) then the Dirach mass is negative!!! In fact in (1) Prob(L > K) should be a decreasing function of K, therefore there are constraints on the base correl model (or rather I should say interpolation/extrapolation method) baseCorr(K) for the that model to be consistent. QuoteOriginally posted by: MrQuantHas anyone tried implementing Local Correlation model by SGI am getting Cummulative Loss Distriution (> 1) for strikes (K > 5%) when I use the market law of losss as being refered in the appendix A.Market Law of Loss states that L(K,BaseCorr) = L(K)+ Skew(K)*Rho(K,BaseCorr)Rho(K,BaseCorr) = Senstivity of Expected Loss on the Equity Tranche (K) to the change in BaseCorrelation
Last edited by
aconze on June 28th, 2005, 10:00 pm, edited 1 time in total.