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...
| Autores: | , , |
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| 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 |
| 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. |
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