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Additional info for Credit Valuation Adjustment
This would involve paying for perfect wrong-way-risk. Positive correlation between the protection seller and the reference credit of exactly one. In some sort of perfect market this should not matter to the buyer if properly corrected for via unilateral or bilateral CVA. But as markets are not perfect a buyer for protection against the credit risk of an entity would find insurance sold by parties other than that entity more competitive than the entity themselves. This also assumes that financial regulation would allow such a contract even over the counter.
At τ the net present value of the (NPV) of the residual payoff until maturity is computed. If τ = τ2 and NPV < 0 (resp. NPV > 0) for the investor (resp. defaulted counterparty), it is fully paid (resp. received) by the investor (resp. defaulted counterparty). If NPV > 0 (resp. NPV < 0) for the investor 25 (resp. defaulted counterparty), only a recovery fraction REC2 of the NPV is exchanged, received (paid) by the investor (defaulted counterparty). If τ = τ0 , and N P V > 0 ( resp. N P V < 0) for the investor (defaulted counterparty), it is fully received (paid) by the investor (defaulted counterparty).
E. the rate at which the present value of the contracted cashflows from the protection and the premium leg are equal. CDS are quoted via ”S”. The discounted payoff of a CDS from the view point of the protection buyer can be thus formalised, Π(t) := 1Ta <τ1