<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

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

Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS)

Department of Mathematics, Art and Science Faculty

Department of Mathematics, Faculty of Education

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On an improved computational solution for the 3D HCIR PDE in finance"}

The aim of this work is to tackle the three–dimensional (3D) Heston– Cox–Ingersoll–Ross (HCIR) time–dependent partial differential equation (PDE)...

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

Published Online: Dec 21, 2019

Page range: 207 - 230

Received: Oct 23, 2018

Accepted: Jan 31, 2019

DOI: https://doi.org/10.2478/auom-2019-0042

Keywords
Financial option pricing, stochastic interest rate, Heston model, non– uniform finite difference method, quadratically convergent

© 2019 Fazlollah Soleymani et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Dec 21, 2019

Page range: 207 - 230

Received: Oct 23, 2018

Accepted: Jan 31, 2019

DOI: https://doi.org/10.2478/auom-2019-0042

KeywordsFinancial option pricing, stochastic interest rate, Heston model, non– uniform finite difference method, quadratically convergent

© 2019 Fazlollah Soleymani et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Financial option pricing, stochastic interest rate, Heston model, non– uniform finite difference method, quadratically convergent