Our corporate CDO transactions possess similar structural features to the standard CDX tranches, but often dif fer with respect to the referenced corporate entities, the term, the attachment points and the detachment points. Therefore, in order to determine the equivalent-risk tranche for each of our corporate CDO transactions, we determine the attachment and detachment points on the CDX index that have comparable estimated probabilities of loss as the attachment and detachment points in our transactions. We begin by performing a simulation analysis of referenced entity defaults in our transactions to determine the probability of portfolio losses exceeding our attachment and detachment points. The referenced entity defaults are primarily determined based on the following inputs: the market observed CDS credit spreads of the referenced corporate entities, the correlations between each of the referenced corporate entities and the term of the transaction. 

For each referenced corporate entity in our corporate CDO transactions, the CDS spreads associated with the term of our transactions (“credit curve”) define the estimated expected loss for each entity (as applied in a market standard approach known as “risk neutral” modeling). The credit curves on individual referenced entities are generally observable. The expected cumulative loss for the portfolio of referenced entities associated with each of our transactions is the sum of the expected losses of these individual referenced entities. With respect to the correlation of losses across the underlying reference entities, two obligors belonging to the same industry or located in the same geographical region are assumed to have a higher probability of defaulting together (i.e., they are more correlated). An increase in the correlations between the referenced entities generally causes a higher expected loss for the portfolio associated with our transactions. The estimated correlation factors that we use are derived internally based on observable third-party inputs that are based on historical data. 

The impact of our correlation assumptions currently does not have a material ef fect on our fair premium estimates in light of the significant impact of our non-performance risk adjustment as described below . 

Once we have established the probability of portfolio losses exceeding the attachment and detachment points in our transactions, we then use the same simulation method to locate the attachment and detachment points on the CDX index with comparable probabilities. These equivalent attachment and detachment points define the equivalent-risk tranche on the CDX index that we use to determine fair premium amounts. 

Determining the Typical Fair Premium Amount —The equivalent-risk tranches for our corporate CDO transactions often are not identical to any standard CDX tranches. As a result, fair premium amounts generally are not directly observable from the CDX index for the equivalent-risk tranche and must be separately determined. We make this determination through an interpolation in which we use the observed premium rates on the standard CDX tranches that most closely match our equivalent-risk tranche to derive the typical fair premium amount for the equivalent-risk tranche. 

Non-Performance Risk Adjustment on Corporate CDOs —The typical fair premium amount estimated for the equivalent- risk tranche represents the fair premium amount for a typical market participant—not Radian. Accordingly, the final step in our fair value estimation is to convert this typical fair premium amount into a fair premium amount for a financial guarantor of similar credit quality to us. A typical market participant is contractually bound by a requirement that collateral be posted regularly to minimize the impact of that participant’ s default or non-performance. This collateral posting feature makes these transactions less risky to the protection buyer , and therefore, priced dif ferently. None of our contracts require us to post collateral with our counterparties, which exposes our counterparties fully to our non-performance risk. We make an adjustment to the typical fair premium amount to account for both this contractual dif ference, as well as for the market’ s perception of our default probability, which is observable through our CDS spread. 

The amount of the non-performance risk adjustment is computed based, in part, on the expected claim payment by Radian. To estimate this expected payment, we first determine the expected claim payment of a typical market participant by using a risk-neutral modeling approach. A significant underlying assumption of the risk-neutral model approach that we use is that the typical fair premium amount is equal to the present value of expected claim payments from a typical market participant. Expected claim payments on a transaction are based on the expected loss on that transaction (also determined using the risk-neutral modeling approach). Radian’ s expected claim payment is calculated based on the correlation between the default probability of the transaction and our default probability . The default probability of Radian is determined from the observed Radian Group CDS spread and the default probability of the transaction is determined as described above under “Defining the Equivalent-Risk Tranche.” The present value of Radian’ s expected claim payments is discounted using a risk-free interest rate, as the expected claim payments have already been risk-adjusted. 

The reduction in our fair premium amount related to our non-performance risk is limited to a minimum fair premium amount, which is determined based on our estimate of the minimum fair premium that a market participant would require to assume the risks of our obligations. Approximately 32% of our corporate CDO contracts as of December 31, 2012 are subject to this minimum fair premium. Our non-performance risk adjustment currently results in a material reduction of our typical fair premium amounts, which in turn has a positive impact on the fair value of these derivatives. 

