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A Positivity-Preserving Splitting Method for 2D Black-Scholes Equations in Stochastic Volatility Models

  • Tatiana P. Chernogorova
  • Radoslav L. Valkov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8236)

Abstract

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.

Keywords

Option Price Stochastic Volatility Global Error Splitting Method Stochastic Volatility Model 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Tatiana P. Chernogorova
    • 1
  • Radoslav L. Valkov
    • 1
  1. 1.Faculty of Mathematics and InformaticsSofia UniversityBulgaria

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