# American Institute of Mathematical Sciences

October  2015, 8(5): 913-931. doi: 10.3934/dcdss.2015.8.913

## Diamond--cell finite volume scheme for the Heston model

 1 Department of Mathematics, Slovak University of Technology, Radlinského 11, 813 68 Bratislava, Slovak Republic 2 Department of Mathematics, Slovak University of Technology, Radlinskeho 11, 813 68 Bratislava, Slovak Republic

Received  December 2013 Revised  July 2014 Published  July 2015

The objective of this article is to propose a novel numerical scheme for solving the partial differential equation arising in the Heston stochastic volatility model. We discretize the governing advection-diffusion-reaction equation using the finite volume technique. The diffusion tensor is treated by means of the diamond--cell approximation. A theoretical result concerning the existence and uniqueness of the solution to the corresponding system of linear equations is proved. Numerical experiments regarding accuracy and order of convergence are shown.
Citation: Pavol Kútik, Karol Mikula. Diamond--cell finite volume scheme for the Heston model. Discrete & Continuous Dynamical Systems - S, 2015, 8 (5) : 913-931. doi: 10.3934/dcdss.2015.8.913
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