论文标题
明确的RKF-COMPACT方案，用于定价制度，以不同的时间步骤切换美国选项
Explicit RKF-Compact Scheme for Pricing Regime Switching American Options with Varying Time Step
论文作者
论文摘要
在这项研究工作中，采用了空间中的四阶紧凑型有限差异方案，并采用了最佳运动边界的高阶分析近似，以解决制度开关定价模型，并采用了四阶紧凑型有限差异方案，并进行了四阶紧凑型有限差异方案。从详细的角度来看，我们将自由边界问题重新验证为具有多固定域的非线性部分微分方程的系统。然后，我们引入了基于平方根函数的转换，具有Lipschitz字符，从中获得高阶分析近似，以计算每个制度中最佳运动边界的衍生物。我们进一步使用四阶空间离散化和自适应时间集成来计算每个制度的边界值，资产选项和选项希腊人。特别是，使用牛顿的Hermite插值估算了耦合资产选项和选项希腊人。最后，使用两次和四项示例进行数值实验，并将结果与现有方法进行比较。从数值实验获得的结果表明，本方法在计算速度和更精确的解决方案方面提供了更好的性能。
In this research work, an explicit Runge-Kutta-Fehlberg (RKF) time integration with a fourth-order compact finite difference scheme in space and a high order analytical approximation of the optimal exercise boundary is employed for solving the regime-switching pricing model. In detail, we recast the free boundary problem into a system of nonlinear partial differential equations with a multi-fixed domain. We then introduce a transformation based on the square root function with a Lipschitz character from which a high order analytical approximation is obtained to compute the derivative of the optimal exercise boundary in each regime. We further compute the boundary values, asset option, and the option Greeks for each regime using fourth-order spatial discretization and adaptive time integration. In particular, the coupled assets options and option Greeks are estimated using Hermite interpolation with Newton basis. Finally, a numerical experiment is carried out with two- and four-regimes examples and results are compared with the existing methods. The results obtained from the numerical experiment show that the present method provides better performance in terms of computational speed and more accurate solutions with a large step size.
