A front-fixing ETD numerical method for solving jump-diffusion American option pricing problems
| Autor: | Rafael Company, Vera N. Egorova, Lucas Jódar |
|---|---|
| Přispěvatelé: | Universidad de Cantabria |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Numerical Analysis
General Computer Science Applied Mathematics Numerical analysis Jump diffusion Finite difference method Boundary (topology) Experimental numerical analysis Gauss quadrature Theoretical Computer Science Quadrature (mathematics) Nonlinear system symbols.namesake American option pricing Modeling and Simulation Ordinary differential equation Finite difference methods symbols Applied mathematics Gaussian quadrature Front-fixing method MATEMATICA APLICADA Exponential time differencing Mathematics |
| Zdroj: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia instname Mathematics and Computers in Simulation, 2021, 189, 69-84 UCrea Repositorio Abierto de la Universidad de Cantabria Universidad de Cantabria (UC) |
| Popis: | [EN] American options prices under jump-diffusion models are determined by a free boundary partial integro-differential equation (PIDE) problem. In this paper, we propose a front-fixing exponential time differencing (FF-ETD) method composed of several steps. First, the free boundary is included into equation by applying the front-fixing transformation. Second, the resulting nonlinear PIDE is semi-discretized, that leads to a system of ordinary differential equations (ODEs). Third, a numerical solution of the system is constructed by using exponential time differencing (ETD) method and matrix quadrature rules. Finally, numerical analysis is provided to establish empirical stability conditions on step sizes. Numerical results show the efficiency and competitiveness of the FF-ETD method. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved. This work has been partially supported by the Ministerio de Ciencia, Innovacion y Universidades, Spanish grant MTM2017-89664-P |
| Databáze: | OpenAIRE |
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