COUNTERPARTY RISK PRICING: IMPACT OF CLOSEOUT AND FIRST-TO-DEFAULT TIMES

In the absence of a universally accepted procedure for the credit valuation adjustment (CVA) calculation, we compare a number of different bilateral counterparty valuation adjustment (BVA) formulas. First we investigate the impact of the choice of the closeout convention used in the formulas. Important consequences on default contagion manifest themselves in a rather different way depending on which closeout formulation is used (risk-free or replacement), and on default dependence between the two entities in the deal. Second we compare the full bilateral formula with an approximation that is based on subtracting two unilateral credit valuation adjustment (UCVA) formulas. Although the latter might be attractive for its instantaneous implementation once one has a unilateral CVA system, it ignores the impact of the first-to-default time, when closeout procedures are ignited. We illustrate in a number of realistic cases both the contagion effect due to the closeout convention, and the CVA pricing error due to ignoring the first-to-default time.