Conversion of upfront CVA into running CVA

The credit value adjustment that crystallises counterparty risk in a derivatives price is generally thought of as an upfront payment, but could equally well be converted into a running premium in appropriate products. But the obvious ways to do this lead to inconsistencies, or are computationally burdensome. Here, Frédéric Vrins and Jon Gregory show how an analytic approximation can get round this

An important consequence of the recent financial crisis is the necessity, due to both market volatility and regulatory constraints, for banks to include counterparty risk in their profit and loss. The adjustment made to the price of an over-the-counter derivatives transaction as a result of the risky nature of their counterparty is known as the credit value adjustment (CVA).

The CVA becomes an effective price factor of a deal, just like the interest rate or the exchange rate, and can often have