Description
A positive correlation between exposure and counterparty credit risk gives rise to the so called Wrong-Way Risk (WWR). Even after a decade of financial crisis, addressing WWR in a both sound and tractable way 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 in mathematical foundations. This is probably the reason why WWR is not explicitly handled in the Basel III regulatory framework inspite of its acknowledged importance. The purpose of this article is to bridge this gap between the approaches used by academics and industry. To this end, we propose a new method to handle WWR: a stochastic correlation approach in modeling WWR. All the methods proposed post financial crisis more often than not use constant correlation to model the dependency between exposure and counterparty credit risk, i.e. assumes a linear dependency, thus fails to capture the tail dependence. Using a stochastic correlation we move further away from Gaussian copula and can capture the tail risk. This can be achieved by modelling the stochastic correlation as a proper transformation of a diffusion process. For our study we calculate the credit valuation adjustment (CVA) by taking a cross currency swap into account which is prone to wrong way risk because of an additional FX risk other than interest rate risk and credit risk. The performance of our approach is illustrated by a thorough comparison with the case when constant correlation model is used. The results show that even supposing perfect correlation between exposure and credit risk the wrong way risk may be underestimated leading to a wrong calculation of CVA. Given the uncertainty inherent to CVA, the proposed method is believed to provide a promising way to handle WWR in a sound and tractable way.