CVA and Wrong-Way Risk: A Model Comparison from a Measure Change Perspective

Abstract

This paper provides three contributions in the context of modeling wrong-way risk (WWR) in counterparty valuation adjustment. First, we show that WWR can be captured by computing unconditonal expectations in another measure. Second, a new dynamic approach called "conic martingale" is proposed, based on the direct modeling of the Azéma supermartingale (out of the Cox setup), allowing for analytical calibration to CDS quotes. Finally, we propose a comparison of WWR exposures and CVA levels between three different approaches (i) a static approach (exposure resampling using a copula), (ii) a stochastic intensity approach and (iii) our conic martingale approach. As our point here is not to precisely model specific exposures, but is instead to draw general conclusions about WWR impact based on results easy to reproduce, the above comparison is performed using prototypical FRA and IRS profiles. The later are modeled through Brownian motion and shifted Brownian bridge, respectively, leading to analytical expressions for WWR expected positive exposures in all three cases.

Keywords: CVA, Wrong-Way risk, stochastic intensity models, bounded martingales

JEL Classification: G13, C22