Numerical valuation of two-asset options under jump diffusion models using Gauss–Hermite quadrature

Autor: M. Fakharany, Vera N. Egorova
Přispěvatelé: Universidad de Cantabria
Rok vydání: 2018
Předmět:
Zdroj: BIRD: BCAM's Institutional Repository Data
instname
Journal of Computational and Applied Mathematics, 2018, 330, 822-834
UCrea Repositorio Abierto de la Universidad de Cantabria
Universidad de Cantabria (UC)
RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
ISSN: 0377-0427
DOI: 10.1016/j.cam.2017.03.032
Popis: [EN] In this work a finite difference approach together with a bivariate Gauss¿Hermite quadrature technique is developed for partial-integro differential equations related to option pricing problems on two underlying asset driven by jump-diffusion models. Firstly, the mixed derivative term is removed using a suitable transformation avoiding numerical drawbacks such as slow convergence and inaccuracy due to the appearance of spurious oscillations. Unlike the more traditional truncation approach we use 2D Gauss¿Hermite quadrature with the additional advantage of saving computational cost. The explicit finite difference scheme becomes consistent, conditionally stable and positive. European and American option cases are treated. Numerical results are illustrated and analyzed with experiments and comparisons with other well recognized methods.
This work has been partially supported by the European Union in the FP7-PEOPLE-2012-ITN program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance) and the Ministerio de Economia y Competitividad Spanish grant MTM2013-41765-P.
Databáze: OpenAIRE
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