On an improved computational solution for the 3D HCIR PDE in finance-Reference-Cited by-同舟云学术

On an improved computational solution for the 3D HCIR PDE in finance

Published:2019-12-01 Issue:3 Volume:27 Page:207-230
ISSN:1844-0835
Container-title:Analele Universitatii "Ovidius" Constanta - Seria Matematica
language:en
Short-container-title:

Author:

Soleymani Fazlollah¹,Akgül Ali²,Akgül Esra Karatas³

Affiliation:

1. Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS) , Zanjan 45137–66731, Iran . soleymani@iasbs.ac.ir

2. Department of Mathematics, Art and Science Faculty , Siirt University , Siirt , Turkey . aliakgul00727@gmail.com

3. Department of Mathematics, Faculty of Education , Siirt University , Siirt , Turkey .

Abstract

Abstract The aim of this work is to tackle the three–dimensional (3D) Heston– Cox–Ingersoll–Ross (HCIR) time–dependent partial differential equation (PDE) computationally by employing a non–uniform discretization and gathering the finite difference (FD) weighting coe cients into differentiation matrices. In fact, a non–uniform discretization of the 3D computational domain is employed to achieve the second–order of accuracy for all the spatial variables. It is contributed that under what conditions the proposed procedure is stable. This stability bound is novel in literature for solving this model. Several financial experiments are worked out along with computation of the hedging quantities Delta and Gamma.

Publisher

Walter de Gruyter GmbH

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