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

Enhancing accuracy for solving American CEV model with high-order compact scheme and adaptive time stepping