The marked branching diffusion algorithm as proposed by (Henry-Labordere, 2012), based on the particle diffusion introduced by (McKean, 1975), is extended upon to include stochastic interest rate models. This extended branching diffusion algorithm is used to solve pricing PDE's for equity derivatives including CVA, using the two types of default conventions as in (Brigo and Morini, 2011). Analytical results are then used to evaluate the performance of the algorithms in the case of one sided payos at maturity in a constant and Hull White interest rate world. An implementation of the lower and upper bounds, as suggested by (Henry-Laborere et al., 2013), for the error introduced by the algorithms polynomial approximation is also given. The main results are the mismatches in price introduced in far out of the money derivatives having value close to zero and the extension to the stochastic interest rate framework.