CVA calculation for CDS on super

The way monoline insurers estimate the FAS 157 credit value adjustments (CVA) on their ABS CDO insurance portfolios vastly overstates the benefits. We propose a simple method that is more accurate, especially when the counterparty default risk is high. The counterparty default recovery rate is also a critical input. Counterparty credit risk is an important topic today with credit crunch affecting increasing number of financial firms. Firms holding super senior piece of ABS CDO would normally hedge their position with a monoline insurer in the form of credit default swap (CDS). Under the stress market conditions for monoline insurers, the effectiveness of the hedge has to be reevaluated based on the credit quality of the counterparty. Credit value adjustment (CVA) is precisely the measurement of counterparty credit risk on OTC derivative transactions. Under the new FAS 157 requirement, counterparties can also adjust their liabilities based on their own credit quality, which leads to the CVA benefits shown on monoline insurers’ quarterly reports when their credit spreads widened a lot due to downgrading below AAA rating. In the usual framework for credit value adjustment calculation, potential future exposure has to be simulated before the adjustment can be calculated (see reference [1]). With all the structural complexities of ABS CDOs, it is not realistic to carry out the simulation in order to calculate CVA. One simple way people would use is to adjust the discount rate curve by the counterparty CDS spread curve. This method is reasonable only when the counterparty CDS spread is small. It is the market convention to quote spread for IG names, but quote price for HY names, because using CDS spread adjusted discount curve is no longer accurate for HY names. The recent mind boggling results of monoline insurers’ quarterly reports on CVA benefits have proven that this simple method has to be improved for stressed counterparties. Here we propose a simplified approach with reasonable accuracy even for stressed names, which will make the calculation easy to implement in the ABS CDO valuation frame work. We make a few assumptions about the model as follows. First, most of the CDS negative basis trades on super senior CDOs were entered at very low spread, which will have a negative mark-to-market value for the protection seller in the foreseeable future. So the counterparty risk will be unilateral on the protection seller, or the monoline insurers. Second, we assume the credit quality of the counterparty is independent of the ABS CDO collateral performance. In reality, this assumption is not necessarily true, in the light of the fact that monoline insurers have been dragged down by the MTM losses 1 Email: [email protected]. The views expressed are the author’s own, not those of AIG. due to their subprime exposures. Assuming all the stress has already been reflected in the CDS spread curves, this is still reasonable. Third, we assume recovery rate R is constant, thus independent of counterparty default or market conditions. This is currently the standard market practice, especially R is normally set to 40%. Under these three assumptions, the standard formula for CVA (see reference [1]) is ∫ − = T t dPD t EE R CVA 0 ) , 0 ( ) ( ) 1 ( (1) where is the risk-neutral discounted expected exposure given by ) (t EE )] ( [ ) ( 0 t E B B E t EE t Q = (2) where is the net present value of future cash flows valued at time and is independent of counterparty default, is the future value of one unit of base currency invested in the money market account. is the risk-neutral probability of counterparty default between time 0 and t with ) (t E t t B ) , 0 ( t PD 0 ) 0 , 0 ( = PD . can be calibrated from the term structure of counterparty CDS spreads. The calibration is based on the assumption of 40% recovery rate for corporate bond. ) , 0 ( t PD Normally firms would have a cash flow model or a correlation model to value their ABS CDO insurance portfolio. We assume essentially is the sum of risk-neutral discounted expected future cash flows at or after time t under the CDS contract. So is the risk-neutral discounted value of the expected cash flow at time t. We have ) (t EE ) (t dEE − ) ) ( )( , 0 ( ) 1 ( ) 0 ( ) 1 ( ) ) ( ))( , 0 ( 1 ( ) 1 ( ) ) ( )( , 0 ( ) 1 ( ) ( ) , 0 ( ) 1 ( ) , 0 ( ) ( ) 1 (