Convergence rate of Markov chains and hybrid numerical schemes to jump-diffusion with application to the Bates model

We study the rate of weak convergence of Markov chains to diffusion processes under quite general assumptions. We give an example in the financial framework, applying the convergence analysis to a multiple jumps tree approximation of the CIR process. Then, we combine the Markov chain approach with other numerical techniques in order to handle the different components in jump-diffusion coupled models. We study the analytical speed of convergence of this hybrid approach and provide an example in finance, applying our results to a tree-finite difference approximation in the Heston and Bates models.