Stability estimates for Discrete duality finite volume scheme of Heston model

by

Stability estimates for Discrete duality finite volume scheme of Heston model

Angela Handlovicova

Slovak University of Technology, Bratislava Slovakia.

DOI:

https://doi.org/10.7494/cmms.2017.2.0596

Abstract:

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. Stability estimates for discrete duality finite volume scheme for proposed model is presented. Numerical experiments using proposed method and comparing it with previous numerical scheme are included

Cite as:

Handlovicova, A. (2017). Stability estimates for Discrete duality finite volume scheme of Heston model. Computer Methods in Materials Science, 17(2), 101 – 110. https://doi.org/10.7494/cmms.2017.2.0596

Article (PDF):

Keywords:

Heston model, Tensor diffusion, Discrete duality finite volume method, Numerical solution, Stability estimates

References:

Andreianov B., Boyer F., Hubert F., 2007, Discrete duality finitevolume schemes for Leray-Lions-type elliptic problemson general 2D meshes, Numer. Methods Partial DifferentialEquations, 2, 1, 145-195.

Black F., Scholes M., 1973, The pricing of options and corporateliabilities, The Journal of Political Economy, 81, 3,637-654.

Domelevo K., Omnes P., 2013, A finite volume method for theLaplace equation on almost arbitrary two-dimensionalgrids, M2AN, 39, 6, 1203-124.

HandloviČová A., 2016, Discrete duality finite volume schemefor solving Heston model, Proccedings of ALGORITMY,264-274.

HandloviČová A., Kotorová D., 2013, Convergence of a semiimplicitdiscrete duality finite volume scheme for thecurvature driven level set equation in 2D, Kybernetika,49, 6, 829-854.

Heston S.L., 1993, A Closed-Form Solution for Options withStochastic Volatility with Applications to Bond and CurrencyOptions. The Review of Financial Studies, 6, 2,327-343.

Kútik P., 2013, Numerical solution of partial differential equationsin financial mathematics, Dissertation Thesis, Bratislava.Kútik P., Mikula K., 2015, Diamond-cell finite volume schemefor the Heston model, Discrete and Continuous DynamicalSystems – Series S (DCDS-S), 8, 913-931.

Olejnik O.A., Radkevich E.V., 1971, Second order equationswith non-negative characteristic form, VINITI Acad. NaukSSSR, Moscow.