Convergence analysis of the discrete duality finite volume scheme for the regularised Heston model

Abstract

<p style='text-indent:20px;'>The aim of the paper is to study problem of financial derivatives pricing based on the idea of the Heston model introduced in [<xref ref-type="bibr" rid="b9">9</xref>]. Following the approach stated in [<xref ref-type="bibr" rid="b6">6</xref>] and in [<xref ref-type="bibr" rid="b7">7</xref>] we construct the regularised version of the Heston model and the discrete duality finite volume (DDFV) scheme for this model. The numerical analysis is performed for this scheme and stability estimates on the discrete solution and the discrete gradient are obtained. In addition the convergence of the DDFV scheme to the weak solution of the regularised Heston model is proven. The numerical experiments are provided in the end of the paper to test the regularisation parameter impact.