Convergence of Option Values under Incompleteness

We study the problem of convergence of discrete-time option values to continuous-time option values. While previous papers typically concentrate on the approximation of geometric Brownian motion by a binomial tree, we consider here the case where the model is incomplete in both continuos and discrete time. Option values are defined with respect to the criterion of local risk-minimization and thus computed as expectations under the respective minimal martingale measures. We prove that for a jump-diffusion model with deterministic coefficients, these values converge; this shows that local risk-minimization processes an inherent stability property under discretization.