Credit valuation adjustment tail risk and the impact of wrong way trades

Actively pricing and hedging credit valuation adjustment (CVA) has quickly emerged as a core function in banks. One of the major functions of the CVA desk is to risk manage CVA. It is well known that wrong way risk has a significant impact on both CVA itself, as well as on the CVA sensitivities (ie the Greeks). This means that wrong way risk can significantly impact the CVA desk hedging strategy. While wrong way risk may have a significant impact on CVA and CVA sensitivity, it is natural to expect that the effect on the tail risk of CVA, and hence the required capital, is even greater. This is an important consideration for the CVA desk as tail risks typically remain unhedged in practice and need to bear capital. In addition, to the extent that a CVA desk tries to hedge some tail risk, this is frequently done in the form of out-of-the money options on either the market instruments (interest rates, foreign exchange (FX), etc.) or credit instruments (credit default swap index or tranches). Since these instruments do not capture the wrong way risk dynamic (they do not have both the market and credit component), they typically are not suitable for completely offsetting the wrong way risk in the CVA book. This paper analyses the impact of wrong way risks on both CVA itself as well as on the tail risks of CVA. It demonstrates that the induced tail risk adjustment to account for wrong-way risk can be more significant than the impact on CVA itself. Hence, the CVA capital impact of wrong way risk can be larger than the CVA pricing impact of the wrong way risk.