Arbitrage-free pricing of CVA for cross-currency swap with wrong-way risk under stochastic correlation modeling framework

A positive correlation between exposure and counterparty credit risk gives rise to the so-called Wrong-Way Risk (WWR). Even after a decade of the financial crisis, addressing WWR in both sound and tractable ways remains challenging. Academicians have proposed arbitrage-free set-ups through copula methods but those are computationally expensive and hard to use in practice. Resampling methods are proposed by the industry but they lack mathematical foundations. The purpose of this article is to bridge this gap between the approaches used by academicians and industry. To this end, we propose a stochastic correlation approach to asses WWR. The methods based on constant correlation to model the dependency between exposure and counterparty credit risk assume a linear dependency, thus fail to capture the tail dependence. Using a stochastic correlation we move further away from the Gaussian copula and can capture the tail risk. This effect is reflected in the results where the impact of stochastic correlation on calculated CVA is substantial when compared to the case when a high constant correlation is assumed between exposure and credit. Given the uncertainty inherent to CVA, the proposed method is believed to provide a promising way to model WWR.