Copula Function Approach

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Li (2000) introduced copula function approach in the aspect of evaluating credit derivatives, the copula function has gradually become the main approach in pricing CDO (Burtschell & George, 2005). In Li (2000) paper, a new random variable named ‘time-until-default’ was created to demonstrate survival time of each defaultable entity. And the copula function approach is based on this random variable to evaluate the default probability of financial instruments. Specifically, copula function specify the joint distribution of the survival times after using the market information to derive the marginal distribution of the survival time. This approach solves the default correlation and the joint distribution of the pool asset to some extent, and it …show more content…
It is because that, with the natural of ‘heavy tail’ in financial asset return, t copula uses the t distribution which is more suitable than the Gaussian copula model. When using the Gaussian copula model for evaluating asset value, default correlation will be underestimated, and this will generate undervalue junior-tranches and overvalue senior-tranches. The t copula with the fat tail feature could produce the more accurate joint default probability and more accurate valuation. And at the end of the paper, it points the drawbacks of the t copula model, which is static evaluation process and the credit spread dynamic cannot be solved in the t copula model. The paper also states that the conditional copula model maybe more appropriate than the t copula …show more content…
And this model is not much relying on the history data as the BET model. The copula approach is directly specifies the dependence structure, through in a specific method (Burtschell & George 2005). The core thought of the copula model is that using the copula function to calculate the joint distribution by known each asset’s default marginal distribution, and then use the Monte Carlo method to evaluate the distribution of aggregate losses. After that, it is straightforward to calculate each tranche’s price under the assumption which is expected value of default leg and expected value of premium leg are equal. The copula model’s formula is introduced as

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