Impact of Stochastic Correlation on CDO Pricing

In CDO pricing, the cross-correlation coefficients play a significant role as it is the sole parameter used. Criticisms are levelled around two features of these correlation coefficients: a dependable data is not available to compute the correlation coefficients between reference obligors; and the same coefficients are used across firms and over the entire life of the CDO while computing the survival, default and hazard probabilities. This strong assumption creates correlation smile and the resultant price is a crude approximation. In this paper, we have attempted to capture the sensitivity of the correlation coefficients in the pricing of CDOs and have also attempted to relax the assumption of the constant correlation coefficients by taking simulated random cross-correlation coefficients to study the effect on pricing. Our results show that the cross-correlation coefficients affect only the premium leg payments and play insignificant role in default leg payment, accrued premium and default losses. When correlation coefficient increases, the premium payable also increases, but at a decreasing rate. If stochastic correlation coefficients are applied, the premium leg and default amounts show a stable pattern, while default payment slightly increases when compared to fixed correlation coefficients