For our corporate CDOs, we estimate the correlation of the default probability between the corporate entities and Radian —the higher the correlation percentage, the higher the probability that both the corporate entities and Radian will default  together. In addition, a widening of the average credit spread increases the expected loss for our transactions, and therefore,  increases the related liability.  For our CDOs of CMBS transactions, we use the CMBX index that most directly correlates to our transaction with  respect to vintage and credit rating and then we estimate losses by applying a correlation factor . Because we own the senior  tranche, an increase in this factor generally increases the expected loss for our transactions and therefore, increases our related  liability.  For our TruPs CDOs, the performance of each underlying reference obligation is measured by a standard and distressed  pricing, which indicates the expected principal recovery . An increase in the standard and stressed principal recovery decreases  the loss severity of the transaction, and therefore, in isolation, decreases the related liability . We also assign these transactions a  probability that we will be required to pay a conditional liquidity claim, which generally would increase our related liability .  For our TruPs-related VIE liabilities, the fair value is estimated using similar inputs as in the estimated fair value of our  TruPs  CDOs, except there is no non-performance risk adjustment as the derivative liability is limited to the segregated assets already  held by the VIE.  For our other non-corporate CDOs, we utilize the internal credit rating, average remaining life and current par outstanding  for each transaction to project both expected losses and an internally developed risk-based capital amount.  An increase in the  average remaining life typically increases the expected loss of the transactions, and therefore, increases our related liability . An  upgrade (downgrade) in the internal credit rating typically decreases (increases) the expected loss of the transactions, and  therefore, decreases (increases) our related liability . For all fair value measurements where we project our non-performance risk, including  VIE debt, we utilize a market  observed credit spread for Radian, which we believe is the best available indicator of the market’ s perception of our non- performance risk. In isolation, a widening (tightening) of this credit spread typically decreases (increases) our related liability .  The assumption used to project our own non-performance risk is independent from the other unobservable inputs used in our  fair value measurements. The net impact on our reported assets and liabilities from increases or decreases in our own credit  spread and from increases or decreases in other unobservable inputs depends upon the magnitude and direction of the changes  in each input; such changes may result in of fsetting effects to our recorded fair value measurements or they may result in  directionally similar impacts, which may be material.  Available for sale securities, trading securities,  VIE debt, derivative instruments and certain other assets are recorded at  fair value. All derivative instruments and contracts are recognized in our consolidated balance sheets as either derivative assets  or derivative liabilities. All changes in fair value of trading securities,  VIE debt, derivative instruments and certain other assets  are included in our consolidated statements of operations.  All changes in the fair value of available for sale securities are  recorded in accumulated other comprehensive income (loss). 207 Radian Group Inc. Notes to Consolidated Financial Statements - (Continued)