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 continuous 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 possesses an inherent stability property under discretization.
Financial support by Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 303 at the University of Bonn, is gratefully acknowledged.
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Runggaldier, W.J., Schweizer, M. (1995). Convergence of Option Values under Incompleteness. In: Bolthausen, E., Dozzi, M., Russo, F. (eds) Seminar on Stochastic Analysis, Random Fields and Applications. Progress in Probability, vol 36. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7026-9_26
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DOI: https://doi.org/10.1007/978-3-0348-7026-9_26
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