Weak and strong error analysis of recursive quantization: a general approach with an application to jump diffusions

Observing that the recent developments of spatial discretization schemes based on recursive (product) quantization can be applied to a wide family of discrete time Markov chains, including all standard time discretization schemes of diffusion processes, we establish in this paper a generic strong error bound for such quantized schemes under a Lipschitz propagation assumption. We also establish a marginal weak error estimate that is entirely new to our best knowledge. As an illustration of their generality, we show how to recursively quantize the Euler scheme of a jump diffusion process, including details on the algorithmic aspects grid computation, transition weight computation, etc. Finally, we test the performances of the recursive quantization algorithm by pricing a European put option in a jump Merton model.