In this research work, we propose a high-order time adapted scheme for pricing a coupled system of fixed-free boundary constant elasticity of variance (CEV) model on both equidistant and locally refined space-grid. The performance of our method is substantially enhanced to improve irregularities in the model which are both inherent and induced. Furthermore, the system of coupled PDEs is strongly nonlinear and involves several time-dependent coefficients that include the first-order derivative of the early exercise boundary. These coefficients are approximated from a fourth-order analytical approximation which is derived using a regularized square-root function. The semi-discrete equation for the option value and delta sensitivity is obtained from a non-uniform fourth-order compact finite difference scheme. Fifth-order 5(4) Dormand-Prince time integration method is used to solve the coupled system of discrete equations. Enhancing the performance of our proposed method with local mesh refinement and adaptive strategies enables us to obtain highly accurate solution with very coarse space grids, hence reducing computational runtime substantially. We further verify the performance of our methodology as compared with some of the well-known and better-performing existing methods.

翻译：本研究提出了一种高阶时间自适应格式，用于在等距和局部加密空间网格上对固定-自由边界常数弹性方差（CEV）耦合系统进行定价。该方法通过增强模型固有及诱导的非正则性，显著提升了性能。此外，耦合偏微分方程组具有强非线性特征，并包含多个时间依赖系数，其中包括早期执行边界的一阶导数。这些系数基于正则化平方根函数推导的四阶解析近似进行逼近。针对期权价值与Delta敏感性的半离散方程，采用非均匀四阶紧致有限差分格式建立。离散耦合系统通过五阶5(4)多曼德-普林斯时间积分方法求解。结合局部网格细化与自适应策略，该方法能够以极粗空间网格获得高精度解，从而大幅降低计算耗时。我们进一步将所提方法与若干现有高性能方法进行了性能对比验证。