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In this paper, we compare static and dynamic (reduced form) approaches formodeling wrong-way risk in the context of CVA. Although all these approachespotentially suffer from arbitrage problems, they are popular (respectively) inindustry and academia, mainly due to analytical tractability reasons. Wecomplete the stochastic intensity models with another dynamic approach,consisting in the straight modeling of the survival (Az\'ema supermartingale)process using the $\Phi$-martingale. Just like the other approaches, thismethod allows for automatic calibration to a given default probability curve.We derive analytically the positive exposures $V^+_t$ "conditional upondefault" associated to prototypical market price processes of FRA and IRS inall cases. We further discuss the link between the "default" condition andchange-of-measure techniques. The expectation of $V^+_t$ conditional upon$\tau=t$ is equal to the unconditional expectation of $V^+_t\zeta_t$. Theprocess $\zeta$ is explicitly derived in the dynamic approaches: it is provento be positive and to have unit expectation. Unfortunately however, it fails tobe a martingale, so that Girsanov machinery cannot be used. Nevertheless, theexpectation of $V^+_t\zeta_t$ can be computed explicitly, leading to analyticalexpected positive exposure profiles in the considered examples.

Wrong-Way Risk Models: A Comparison of Analytical Exposures