Computing credit valuation adjustment solving coupled PIDEs in the Bates model

Credit Value Adjustment is the charge applied by financial institutions to the counter- party 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 in The Review of Financial Studies 9(1): 69–107, 1996), which considers an underlying affected by both stochas- tic volatility and random jumps. We propose an efficient method which improves the Finite-Difference Monte Carlo (FDMC) approach introduced by de Graaf et al. (Jour- nal of Computational Finance 21, 2017) 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 which is done by employing the Hybrid Tree-Finite Difference method developed by Briani et al. (arXiv:1603.07225 2016;IMA Journal of Man- agement Mathematics 28(4): 467–500, 2017;The Journal of Computational Finance 21(3): 1–45, 2017). Moreover, the direct application of the hybrid techniques in the original FDMC approach is also considered for comparison purposes. Several numer- ical tests prove the effectiveness and the reliability of the proposed approach when both European and American options are considered. Subject classification numbers as needed.