Approximation of stochastic differential equations driven by alpha-stable Levy motion

Aleksander Janicki, Zbigniew Michna and Aleksander Weron

No HSC/96/02, HSC Research Reports from Hugo Steinhaus Center, Wroclaw University of Science and Technology

Abstract: In this paper we present a result on convergence of approximate solutions of stochastic differential equations involving integrals with respect to alpha-stable Levy motion. We prove an appropriate weak limit theorem, which does not follow from known results on stability properties of stochastic differential equations driven by semimartingales. It assures convergence in law in the Skorokhod topology of sequences of approximate solutions and justifies discrete time schemes applied in computer simulations. An example is included in order to demonstrate that stochastic differential equations with jumps are of interest in constructions of models for various problems arising in science and engineering, often providing better description of real life phenomena than their Gaussian counterparts. In order to demonstrate the usefulness of our approach, we present computer simulations of a continuous time alpha-stable model of cumulative gain in the Duffie–Harrison option pricing framework.

Keywords: Stable distribution; Simulation; Stochastic differential equation (SDE); Option pricing (search for similar items in EconPapers)
JEL-codes: C15 C16 (search for similar items in EconPapers)
Pages: 20 pages
Date: 1996
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published in Applicationes Mathematicae 24.2 (1996) 149-168

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http://matwbn.icm.edu.pl/ksiazki/zm/zm24/zm2424.pdf Final printed version, 1996 (application/pdf)

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Persistent link: https://EconPapers.repec.org/RePEc:wuu:wpaper:hsc9602

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