Euler-Maruyama approximations in mean-revertingstochastic volatility model under regime-switching

摘要

Stochastic differential equations (SDEs) under regime-switchinghave recently been developed to model various financialquantities. In general, SDEs under regime-switching have noexplicit solutions, so numerical methods for approximations havebecome one of the powerful techniques in the valuation offinancial quantities. In this paper, we will concentrate on theEuler-Maruyama (EM) scheme for the typical hybrid mean-revertingθ-process. To overcome the mathematical difficultiesarising from the regime-switching as well as the non-Lipschitzcoefficients, several new techniques have been developed in thispaper which should prove to be very useful in the numericalanalysis of stochastic systems.