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Base Correlation Normal copula model has become the market standard to compute the joint default probabilities of a collateral pool, which is essential to value a CDO trade [4,5]. Within the GSP credit derivative modeling framework, a normal copula Monte Carlo (MC) simulation model has already implemented The normal copula function is a multivariate cumulative normal distribution with correlation matrix . Applying the normal copula function to the modelling of correlated default events of a collateral asset pool, the uniform random variables are mapped to the default probabilities with standard normal distribution. The default copula, or the cumulative joint default probability for the collateral pool with n assets, can be expressed The normal copula function is actually an n-dimensional integral, which is hard to calculate directly if n is large. We use the one-factor normal copula model to reduce the dimensionality in order to achieve an analytical solution In order to price a CDO tranche with an attachment point and a detachment point , the expected loss function of the tranche is introduced, which has the form In order to calculate the expected loss function denoted in Eq. (13), we need to the find the probability distribution function of the loss function. In general there are two approaches: 1) via the characteristic function and the moment generating function and 2) via iteration.
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