Simulating Multiple Defaults and Migration II: Credit value adjustment of credit default swaps
by Chuang Yi of the Royal Bank of Canada
April 14, 2010
Abstract: Yi (2009b) proposed an efficient algorithm for simulating joint defaults and migration based on the first passage times of multivariate Brownian motions. In this article, we extend this algorithm to a multi-step simulation that utilizes a minimal approximation for the CVA calculation. We then study the credit value adjustment (CVA) for credit default swaps (CDS) using this multi-step simulation. In particular, the sensitivities of CVAs with respect to input parameters are anaylzed in details. We numerically confirm that both unilateral and bilateral CVA of one party increase as its counterparty's creditworthiness deteriorates. The order of the creditworthiness of the three parties involved is found to be relevant for the sensitivities of the CVAs with respect to distance-to-default (DD) correlations. Theoretical justification is also provided. The designed simulation algorithm can easily be applied to calculate CVAs at counterparty level for a pool of over-the-counter (OTC) instruments from different markets such as Equity, IR, FX and Commodity. This is described in details in a companion paper titled: Simulating Joint Defaults and Migration III: Comprehensive Credit Value Adjustment System.
Keywords: Credit Value Adjustment, Credit Default Swaps, Right/Wrong Way Risk, Joint Defaults and Migration, Distance to Default.