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Hi,I was going through the paper "Valuation of a CDO and an nth to Default CDS Without Monte Carlo Simulation". I completely fail to understand something which has been considered trivial or common knowledge as to how does one actually use the systematic factor 'M' in the one factor Gaussian Model when one is actually implementing i.e., coding the model.In the equation: Prob(ti<t|M) = H [(Finv[Q(t)] - ai*M)/sqrt(1-ai^2))]...we know that M is Standard Normal Variate N(0,1). But thats it. How do we actually use this to calculate Prob(ti<t|M)?How many values of M do we have to consider?How do we numerically "integrate" over all values of M? Is it merely a summation?Can some one clearly specify the steps that need to be followed in the same? That will help me a LOT as this question is stopping me from coding the model!Thanks!!!!!!Tarun

Hi tarunmakhija,Use a numerical integration : Gauss-Hermite with 20 points is suitable.(see->http://www.efunda.com/math/num_integrat ... ermite.cfm) But you need to integrate \pi_T(k|M) (i.e. not Prob(ti<t|M) separetely, because defaults are independant conditionally to M). I coded this model in C++, you can ask me for other details.Péniel

IMHO 20 Gauss-Hermite nodes is not sufficient for a 1-factor model with a realistic portfolio (i.e., not homogeneous). 48 would be much better. Also, the standard GH integrator needs to be modified to account for integration with respect to a standard normal density instead of exp(-x^2). This can be accomplished by multiplying the standard abscissa by sqrt(2) and dividing the final result by sqrt(pi).

could you send me your codethank youmy e-mail:g692515019@ccu.edu.tw

Hi Peneil,Thanks. I will read through what you sent and shoot some more queries. Is it possible for you to send me your C++ implementation? That would be really helpful in understanding the implementation nuances. My email id is: tarun.makhija@gmail.com .. Thanks,Tarun