Radian Group Inc. Notes to Consolidated Financial Statements - (Continued) For markets in which inputs are not observable or limited, we use significant judgment and assumptions that a typical  market participant would use to evaluate the market price of an asset or liability . Given the level of judgment necessary , another  market participant may derive a materially dif ferent estimate of fair value.  These assets and liabilities are classified in Level III  of our fair value hierarchy . For fair value measurements categorized within Level III of the fair value hierarchy , we use certain  significant unobservable inputs in estimating fair value.  Those inputs primarily relate to the probability of default, the expected  loss upon default and our own non-performance risk as it relates to our liabilities.  The following table summarizes the  significant unobservable inputs used in our recurring Level III fair value measurements as of  December 31, 2012: (In millions) Fair Value December 31, 2012 (1) Valuation Technique Unobservable Input Range/ Weighted Average Level III Investments: State and municipal obligations . $ 19.0 Discounted cash flow Discount rate 8.8% Expected loss 19.0% Other investments . . . . . . . . . . . 78.0 Discounted cash flow Discount rate 1.9% Level III Derivative Assets: Corporate CDOs. . . . . . . . . . . . . 8.8 Base correlation model Radian correlation to corporate index 85.0% Average credit spread <0.1% - 2.7% Own credit spread (2) 8.0% - 9.1% CDOs of CMBS. . . . . . . . . . . . . 1.6 Discounted cash flow Radian correlation to CMBS transaction index 72.0% - 85.0% Own credit spread (2) 8.0% - 9.1% TruPs CDOs. . . . . . . . . . . . . . . . 1.6 Discounted cash flow Principal recovery 65.0% Principal recovery (stressed) 60.0% Probability of conditional liquidity payment 0.8% - 36.7% Own credit spread (2) 8.0% - 9.1% NIMS derivative assets . . . . . . . 1.6 Discounted cash flow NIMS credit spread 44.0% Own credit spread 8.5% 205