SFB 303 Discussion Paper No. B - 333
Author: Runggaldier, Wolfgang J., and Martin Schweizer
Title: Convergence of Option Values under Incompleteness
Abstract: 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.
Keywords: option pricing, incomplete markets, convergence, minimal martingale measure, locally risk-minimization trading strategies, jump-diffusion
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