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

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 usi...

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Detalles Bibliográficos
Autores: Fakharany, M., Egorova, V., Company, R.
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2017
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/688
Acceso en línea:http://hdl.handle.net/20.500.11824/688
https://doi.org/10.1016/j.cam.2017.03.032
Access Level:acceso abierto
Palabra clave:Two-asset option pricing
Partial-integro differential equation
Jump-diffusion models
Numerical analysis
Bivariate Gauss–Hermite quadrature
Descripción
Sumario: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 analysed with experiments and comparisons with other well recognized methods.