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## CVA – Which way is the wrong-way?

Currently, the mandated formula for the calculation for CVA, for regulatory purposes, is as follows

Which equates to

Where is the probability of default between time and . For further definitions of the variables in the equation see Basel III. pg 31 – 32.

Basel III enforces recognition of Wrong-way risk. Wrong-way risk is the state of the value of the reference asset being high when the probability of default by the counterparty is high. The implications of Wrong-way risk are that the effective exposure is increased (captured through an adjustment factor, and in some cases, where there are legal links between the counterparty and the underlying reference asset for the derivatives trade, this is also achieved through a loss given default of 100%.

A market risk capital charge is calculated by simulating the market variables in the CVA calculation (LGD, credit spreads) across the institutions specific market risk calculation, as well as recalibrating, and estimating expected exposure, for a market stress period. A VaR result for this simulation is then calculated and represents the banks capital charge for CVA VaR.

There are two issues regarding wrong-way risk in Basel III. Firstly, the use of LGD, or to reflect the wrong-way risk implies that the exposure is fixed across simulations of the counterparties’ credit-worthiness. A fixed number reflects the increased exposure across all scenarios. For the sophisticated CVA desk, hedging both the exposure and the probability of default simultaneously, the hedging activities of the desk will not necessarily be accurately captured in the CVA VaR charge.

Secondly, there is no recognition of right-way risk. To borrow the example from Basel III, and turn it around, in the case that a counterparty issues call warrants on it’s own stock, provided the strike price is of a sufficiently high level, there is almost no chance that the counterparty will default, and the call options be in the money. Although the CVA charge should be 0 in this case, from a regulatory standpoint it will not be, and capital would need to be held against the CVAs market risk. Either the CVA charge can be taken, and the default risk need not be hedged by the desk, or the desk is in a position to now offer more competitive pricing on the trade.

Basel III effectively assumes that the reference asset value and the probability of default of the counterparty are independent. It then makes an adjustment to the CVA charge to account for the case where the two values are positively correlated. The document is rightly sceptical of assumed correlation or causality between two separate market variables, and the associated capital charges may be unavoidable. However, in the face of compelling evidence of a statistical relationship (or indeed practical or legal) between the reference asset and derivatives counterparty, the sophisticated CVA trader may very well trade according to a separate CVA calculation which reflects this relationship.