Abstract 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.

中文翻译：

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一种求解跳跃扩散美式期权定价问题的前置ETD数值方法

摘要 跳跃扩散模型下的美式期权价格由自由边界偏积分微分方程 (PIDE) 问题决定。在本文中，我们提出了一种由几个步骤组成的前端固定指数时间差分（FF-ETD）方法。首先，通过应用前固定变换将自由边界包含在方程中。其次，产生的非线性 PIDE 是半离散化的，从而形成常微分方程 (ODE) 系统。第三，利用指数时间差分（ETD）方法和矩阵求积规则构造了系统的数值解。最后，提供数值分析以建立关于步长的经验稳定性条件。数值结果显示了 FF-ETD 方法的效率和竞争力。