We investigated different ways to model the dependence between the credit and other market risk components in hybrid derivatives.
To do so, we used both structural and reduced–form frameworks for credit risk modelling. In particular, we applied results from Analytically Tractable First–Passage (AT1P) model — a model belonging to the family of structural approaches — to the pricing of Contingent Conversion bonds and a reduced– form approach to the pricing of quanto Credit Default Swaps (CDS).
With respect to the former problem, we proposed a method to incorporate regulatory capital information into an AT1P–based model.
With respect to the latter, we showed how to derive coupled two–dimensional PDE systems to price quanto CDSs in reduced form approaches. Furthermore, we investigated the impact of jumps to default on the FX/credit dependence structure, arguing that this is necessary mechanism to explain the observed quanto CDS spreads on Italian Republic during the Euro–debt cri-
sis of 2011–2012. We proved that an invariance property of the FX rate with respect to replacing it with its reciprocal rate is satisfied by our proposed, jump–to–default / diffusion, model.
Finally, we applied both approaches to Credit Valuation Adjustment (CVA) estimation, where we discussed the modelling–choice impact on the wrong–way risk estimation.