Radian Group Inc. Notes to Consolidated Financial Statements - (Continued) 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.  Non-Corporate CDOs and Other Derivative Transactions Our non-corporate CDO transactions include our guaranty of  TruPs CDOs, CDOs of ABS, CDOs of CMBS and CDOs  backed by other asset classes such as: (i) municipal securities; (ii) synthetic financial guarantees of  ABS; and (iii) project  finance transactions. The fair value of our non-corporate CDOs and other derivative transactions is calculated as the dif ference  between the present value of the expected future contractual premiums and our estimate of the fair premium amount for these  transactions. The present value of expected future contractual premiums is determined based on the methodology described  above for corporate CDOs. The contractual premiums associated with87% of the aggregate net par outstanding of our non- corporate CDO contracts are subject to change due to counterparties being provided the right to terminate these transactions.  We also cap the total estimated fair value of the contracts subject to termination such that none of these contracts are in a  derivative asset position. As of December 31, 2012,34% of the aggregate net par outstanding of our non-corporate CDO  transactions was capped in this manner . In all other instances, we utilize internal models to estimate the fair premium amount  as described below. These credit derivatives are categorized in Level III of the fair value hierarchy . 199