  Credit value adjustment (CVA) is the charge applied by financial institutions
to the counterparty to cover the risk of losses on a counterpart default event.
In this paper we estimate such a premium under the Bates stochastic model
(Bates [4]), which considers an underlying affected by both stochastic
volatility and random jumps. We propose an efficient method which improves the
finite-difference Monte Carlo (FDMC) approach introduced by de Graaf et al.
[11]. In particular, the method we propose consists in replacing the Monte
Carlo step of the FDMC approach with a finite difference step and the whole
method relies on the efficient solution of two coupled partial
integro-differential equations (PIDE) which is done by employing the Hybrid
Tree-Finite Difference method developed by Briani et al. [6, 7, 8]. Moreover,
the direct application of the hybrid techniques in the original FDMC approach
is also considered for comparison purposes. Several numerical tests prove the
effectiveness and the reliability of the proposed approach when both European
and American options are considered.
