Stress Test of Counterparty Risks and Dynamic Hedging of the CVA

Eduardo Canabarro

In this chapter we discuss the design of the stress test for counterparty credit risk (CCR). In particular, we focus on a risk component that has not been addressed directly by the usual stress tests of counterparty risks: the costs incurred by a bank that hedges its credit valuation adjustment (CVA) dynamically. We build a Monte Carlo simulation model to analyse these costs. The results of our model show that a combination of market volatility, market illiquidity, transaction costs and wrong-way risks can lead to CVA hedging costs that are very large and even larger than the full value of the initial CVA. We analyse the interaction between the frequency of the rebalancing of the CVA hedges and the costs and errors of the dynamic hedging strategy. In the presence of transaction costs there is a trade-off between hedging error, which is higher at lower rebalancing frequencies, and transactions costs. Our results can be framed in the context of the literature on option replication with transaction costs, eg, Leland (1985) and Boyle and Vorst (1992).

The chapter is organised as follows: first, we summarise the evolution of the regulatory framework for stress testing, which