A front-fixing ETD numerical method for solving jump-diffusion American option pricing problems

被引：10

作者：

Company, Rafael ^{[1
]}

Egorova, Vera N. ^{[2
]}

Jodar, Lucas ^{[1
]}

机构：

[1] Univ Politecn Valencia, Inst Matemat Multidisciplinar, Camino Vera S-N, Valencia 46022, Spain

[2] Univ Cantabria, Dept Matemat Aplicada & Ciencias Computac, Avda Castros S-N, Santander 39005, Spain

来源：

MATHEMATICS AND COMPUTERS IN SIMULATION | 2021年 / 189卷

关键词：

American option pricing; Front-fixing method; Exponential time differencing; Finite difference methods; Experimental numerical analysis; Gauss quadrature; FINITE-DIFFERENCE SCHEME; STOCHASTIC VOLATILITY; IMPLICIT; MODEL;

D O I：

10.1016/j.matcom.2020.07.015

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

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.

引用

页码：69 / 84

页数：16

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