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We study the rate of weak convergence of Markov chains to diffusion processesunder suitable but quite general assumptions. We give an example in thefinancial framework, applying the convergence analysis to a multiple jumps treeapproximation of the CIR process. Then, we combine the Markov chain approachwith other numerical techniques in order to handle the different components injump-diffusion coupled models. We study the speed of convergence of this hybridapproach and we provide an example in finance, applying our results to atree-finite difference approximation in the Heston or Bates model.

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