In this paper we present a locally one-dimensional (LOD) splitting method to the two-dimensional Black-Scholes equation, arising in the Hull & White model for pricing European options with stochastic volatility. The parabolic equation degenerates on the boundary x = 0 and we apply to the one-dimensional subproblems the fitted finite-volume difference scheme, proposed in [8], in order to resolve the degeneration. Discrete maximum principle is proved and therefore our method is positivity-preserving. Numerical experiments are discussed.
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