Modeling credit value adjustment with downgrade-triggered termination clause using a ruin theoretic approach

Abstract

Downgrade-triggered termination clause is a recent innovation in credit risk management to control counterparty credit risk. It allows one party of an over-the-counter derivative to close off its position at marked-to-market price when the other party’s credit rating downgrades to an agreed alarming level. Although the default risk is significantly reduced, the non-defaulting party may still suffer losses in case that the other party defaults without triggering the termination clause prior to default. At the heart of the valuation of credit risk adjustment(CVA) is the computation of the probability of default. We employ techniques from ruin theory and complex analysis to provide solutions for probabilities of default, which in turn lead to very efficient and accurate algorithms for computing CVA. The underlying risk model in question is an extension of the commercially available KMV–Merton model and hence can be easily implemented. We provide a hypothetical example of CVA computation for an interest-rate swap with downgrade-triggered termination clause. The paper also contributes to ruin theory by presenting some new results on finite-time ruin probabilities in a jump-diffusion risk model.