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：本文提出一种高阶时间自适应格式，用于在均匀网格与局部加密空间网格上对固定-自由边界常数弹性方差（CEV）模型的耦合系统进行定价。该方法显著提升了模型固有及诱导不规则性的处理性能。此外，该耦合偏微分方程组具有强非线性特征，涉及多个与早期行权边界一阶导数相关的时间依赖系数。基于正则化平方根函数推导的四阶解析逼近方法可近似求解此类系数。采用非均匀四阶紧致有限差分格式获得期权价值与Delta敏感性的半离散方程，并利用五阶5(4)多曼德-普林斯时间积分方法求解耦合离散方程组。通过结合局部网格加密与自适应策略，所提方法在极粗空间网格上即可获得高精度解，从而大幅降低计算耗时。我们进一步与现有知名且性能较优的方法进行对比验证了本方法的性能。