Credit default swaps valuation

While it is not uncommon for active market makers and end users to utilize their own, customized set of tools for credit default swap valuation, many, if not all of these methodologies arise from the same general framework and ask the same two questions What is the probability that a particular issuer will default and, Upon the occurrence of a default event, what does one expect to recover from an issuer ... 

Cash settlement represents another method of settling credit derivative transactions. In cash settlement, the protection buyer will receive an amount based on the difference between par and the valuation of the reference asset at a given valuation date, as agreed in the credit default swap contract. 

A credit default swap has two valuation legs, the fee leg and the contingent leg. We can develop an equation of value which describes the valuation of the credit default swap (assuming a deterministic recovery rate) as... 

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