Hello,I have implemented the Hull and White model [Valuation of a CDO and an nth to Default CDS Without Monte Carlo Simulation]...I used a 30 point Gaussian Quadrature for numerical integration. As you would see from the results below, except for the equity tranche, the results for other tranches look fairly accurate. I am not sure if this is due to the numerical integration technique. I'll really appreciate any ideas/hints.Hull and White Implementation Results [correlation 0.40]-------------------------------------------------equity : 26.3 %mezz 4 : 4.34 %mezz 3 : 2.27 %mezz 2 : 1.16 %mezz 1 : 0.35 %My Implementation Results [correlation 0.40]----------------------------------equity : 23.87 %mezz 4 : 4.39 %mezz 3 : 2.25 %mezz 2 : 1.22 %mezz 1 : 0.35 %Thanks,Tarun Makhija

I would try changing the number of points in your Gaussian Quadrature and seeing how stable your results are when you do this.

It is typical to use 48 nodes for the 1-factor Gaussian copula. The examples in the paper are simplistic and I would not recommend choosing the number of nodes in general based upon it.I wouldn't worry about matching results from Hull exactly. There are many little details that are not explained in the paper that have some impact on the results, including the integration scheme, discount factors, accrual factors, ...

Thank you.Well, the difference for the equity tranche is about 200bps no matter what correlation I use (thats what worries me.). It is relatively very stable for the Mezzanine tranches as you would see from the results below for different correlations. I will try the 48 node integration and vary it further and see how stable the results are as you guys have suggested.For correlation 0.40==============Hull and White Implementation Resultstranche 5 : 26.3 %tranche 4 : 4.34 % tranche 3 : 2.27 % tranche 2 : 1.16 %tranche 1 : 0.35 %My Implementation Resultstranche 5 : 23.87 % tranche 4 : 4.39 % tranche 3 : 2.25 % tranche 2 : 1.22 %tranche 1 : 0.35 %For correlation 0.30==============Hull and White Implementation Resultstranche 5 : 34 % tranche 4 : 4.53 % tranche 3 : 1.98 % tranche 2 : 0.89 % tranche 1 : 0.18 %My Implementation Resultstranche 5 : 31.26 % tranche 4 : 4.61 % tranche 3 : 1.99% tranche 2 : 0.92 % tranche 1 : 0.18 %For correlation 0.20==============Hull and White Implementation Resultstranche 5 : 42.6 % tranche 4 : 4.55 % tranche 3 : 1.51 % tranche 2 : 0.51 % tranche 1 : 0.06 %My Implementation Resultstranche 5 : 39.68 % tranche 4 : 4.65 % tranche 3 : 1.54 % tranche 2 : 0.53 % tranche 1 : 0.06 %For correlation 0.10==============Hull and White Implementation Resultstranche 5 : 53 % tranche 4 : 4.18 % tranche 3 : 0.76 % tranche 2 : 0.13 % tranche 1 : 0.00 %My Implementation Resultstranche 5 : 49.86 % tranche 4 : 4.31 % tranche 3 : 0.79 % tranche 2 : 0.13 % tranche 1 : 0.004 %