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Normal Copula As a well known default correlation model, the normal copula provides an alternative method to the Poisson model in generating correlated default events of a collateral pool. It is implemented using the Monte Carlo (MC) simulation. The testing was conducted by implementing an independent test model using the MC simulation. The results of two sample trades, generated by the test model and the model, respectively, were compared. The MC implementation was also verified by the closed form solutions and the Poisson model. The model implements the normal copula which is a default correlation model. Implemented by Monte Carlo (MC) simulation, the model generates correlated default events of a collateral pool of obligors, hence can be used to value basket default swaps and Collateral Debt Obligations (CDOs) (nofm basket, FirstLoss, Caribou, and MezzMezzMezz). Along with the normal copula implementation, the spreadsheet model has changed the way of generating interest rate curves and credit curves. The interest rate curves and credit spreads are retrieved directly from the Infinity database. The credit curve is calculated using a C++ dll function in which the same algorithm and methodology as that of Infinity is employed. This new implementation will bring interest rate curve and the credit curve generation in the spreadsheet model consistent with Infinity. The new implementation is also much faster than the original curve generation implementation of the spreadsheet model. Because the obligors in the collateral pool of the test trade are homogeneous with flat correlation, we could value the trade using one factor normal copula model. In the test trade the principal of the first tranche equals loss given default (LGD) of the obligor ($6,000,000). This makes the value of protection for the first tranche equivalent to that of a first to default basket. According to the theory shown above, the joint survival function of the first to default event for a collateral pool with n obligors is provided However, when the asset correlation is zero, each obligor is independent and there is no correlated default event at all. On the other hand, if the obligors are assumed to be homogenous, as the case of the test trade, and the asset correlation is assumed to be one, all the obligors in the collateral pool are perfectly correlated and should behave like one obligor. In a scenario either all the obligors default at the same time or no one defaults. In such two cases, same results should be predicted no matter what default correlation models are employed.
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