# Discrete duality finite volume scheme for solving Heston model

## Main Article Content

## Abstract

New numerical scheme for tensor diffusion equation based on discrete duality finite volume (DDFV) method is derived. Tensor diffusion equation represents an important model in many fields of science. We focused our attention to the problem which arises in financial mathematics and is known as 2D Heston model see [5]. Existence and uniqueness of numerical solution is derived and numerical experiment using proposed scheme are included.

## Article Details

How to Cite

HANDLOVIČOVÁ, Angela.
Discrete duality finite volume scheme for solving Heston model.

**Proceedings of the Conference Algoritmy**, [S.l.], p. 264-274, feb. 2016. Available at: <http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/415>. Date accessed: 22 sep. 2017.
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## References

[1] B. Andreianov and F. Boyer and F. Hubert, Discrete duality finite volume schemes for Leray-Lions-type elliptic problems on general 2D meshes, Numer. Methods Partial Differential Equations, Vol. 2, No. 1, (2007), pp. 145–195.

[2] B. Andreianov, M. Bendahmane, K.H. Karlsen Discrete duality finite volume schemes for doubly nonlinear degenerate hyperbolic-parabolic equations Journal of Hyperbolic Differential equations, Vol. 7 No. 1 (2010) pp. 1-67

[3] K. Domelevo and P. Omnes, A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids, M2AN, Vol. 39 No 6, (2013), pp. 1203-124.

[4] A. Handlovičová and D. Kotorová, Convergence of a semi-implicit discrete duality finite volume scheme for the curvature driven level set equation in 2D, Kybernetika, Vol 49. No. 6, (2013), pp. 829-854.

[5] P. Kútik and K. Mikula, Diamond-cell finite volume scheme for the Heston model, Discrete and Continuous Dynamical Systems Series S (DCDS-S) Vol. 8, No. 5 (2015) pp. 913 931.

[6] M. Zboranová, Metóda konečných objemov na riešenie vybraných modelov

finančnej matematiky, Diploma thesis STU Bratislava (2014)

[2] B. Andreianov, M. Bendahmane, K.H. Karlsen Discrete duality finite volume schemes for doubly nonlinear degenerate hyperbolic-parabolic equations Journal of Hyperbolic Differential equations, Vol. 7 No. 1 (2010) pp. 1-67

[3] K. Domelevo and P. Omnes, A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids, M2AN, Vol. 39 No 6, (2013), pp. 1203-124.

[4] A. Handlovičová and D. Kotorová, Convergence of a semi-implicit discrete duality finite volume scheme for the curvature driven level set equation in 2D, Kybernetika, Vol 49. No. 6, (2013), pp. 829-854.

[5] P. Kútik and K. Mikula, Diamond-cell finite volume scheme for the Heston model, Discrete and Continuous Dynamical Systems Series S (DCDS-S) Vol. 8, No. 5 (2015) pp. 913 931.

[6] M. Zboranová, Metóda konečných objemov na riešenie vybraných modelov

finančnej matematiky, Diploma thesis STU Bratislava (2014)