Radian Group Inc. Notes to Consolidated Financial Statements - (Continued) We established a fair value hierarchy by prioritizing the inputs to valuation techniques used to measure fair value.  The  hierarchy gives the highest priority to unadjusted quoted prices in active markets for identical assets or liabilities (Level I  measurements) and the lowest priority to unobservable inputs (Level III measurements).  The three levels of the fair value  hierarchy under this standard are described below: Level I  — Unadjusted quoted prices for identical assets or liabilities in active markets that are accessible at the  measurement date for identical, unrestricted assets or liabilities; Level II — Prices or valuations based on observable inputs other than quoted prices in active markets for identical  assets and liabilities; and Level III — Prices or valuations that require inputs that are both significant to the fair value measurement and  unobservable. The level of market activity used to determine the fair value hierarchy is based on the availability of observable inputs  market participants would use to price an asset or a liability , including market value price observations. 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 different estimate of fair value.  These assets and liabilities are classified in Level III of our fair value hierarchy . Available for sale securities, trading securities,  VIE debt, derivative instruments and certain other assets are recorded at  fair value as described in Note 5.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). Insurance Premiums-Revenue Recognition Mortgage insurance premiums written on an annual and multi-year basis are initially recorded as unearned premiums and  earned over the policy term. Premiums written on a monthly basis are earned over the period that coverage is provided.  Annual  premiums are amortized on a monthly , straight-line basis. Multi-year premiums are amortized over the terms of the contracts in  relation to the anticipated claim payment pattern based on historical industry experience. In connection with our insurance  rescission activity, we refund premiums to our lender customers. Ceded premiums written are initially set up as prepaid  reinsurance and are amortized in a manner consistent with how direct premiums are earned. Premiums on certain structured  transactions in our mortgage insurance business are recognized over the period that coverage is provided. In our financial guaranty business, insurance premiums are earned in proportion to the level of amortization of insured  principal over the contract period or over the period that coverage is provided. Unearned premiums represent that portion of  premiums that will be earned over the remainder of the contract period.  We record the initial unearned premium liability on  installment policies equal to the present value of the premiums due or expected to be collected over either the period of the  policy or the expected period of risk. In determining the present value of premiums due, we use a discount rate that reflects the  risk-free rate. Premiums paid in full at inception are recorded as unearned premiums. In addition, we recognize the remaining  unearned premium revenue when bonds issued are redeemed or otherwise retired (“refundings”) that results in the  extinguishment of the financial guaranty policies insuring such bonds.  A refunding that is ef fected through the deposit of cash  or permitted securities into an irrevocable trust for repayment, when permitted under the applicable bond indenture (a “legal  defeasance”), does not qualify for immediate revenue recognition since the defeased obligation legally remains outstanding and  covered by our insurance. See Note 12 for further information.  Assumed premiums are based on information reported by  ceding companies. Premiums ceded through reinsurance agreements reduce premiums earned in a manner that is consistent  with the recognition of the gross premiums as described above.When insured obligations are refunded or called, the remaining  premiums are generally earned at that time. Credit enhancement fees earned on derivative contracts are included in the change in fair value of derivative instruments. 183