CCR KVA Relief Through CVA: A Regression‐Based Monte Carlo Approach

We present and examine, by example of a USD interest rate swap and a EUR/USD cross‐currency basis swap, a regression‐based Monte Carlo approach to counterparty credit default risk (CCR) capital and CCR capital valuation adjustment (KVA) calculations [assuming the standardized approach to counterparty credit risk for exposura‐et‐default (SA‐CCR EAD) and the internal ratings‐based (IRB) approach for CCR risk weights]. This approach allows to incorporate the capital lowering effect of credit valuation adjustment (CVA) in an efficient manner, without having to resort to lengthy nested Monte Carlo simulations. We find that the regression‐based Monte Carlo approach works well in most situations. In other situations, the accuracy of the approach is sensitively controlled by the choice of explanatory variables. We discuss in detail the conditions and underlying dynamics under which this happens. In computing and presenting a selection of numerical examples, we also explore the impact of dynamic CCR risk weights on CCR KVA, and compare regression‐based CCR KVA results with CCR KVA results from nested Monte Carlo, alternative frequently used CCR KVA simplifications, and standardized CVA KVA.