A New High-Order Compact Finite Difference Scheme for American-Style Options: Partial HOCJ

The paper presents a simple yet powerful numerical scheme, partial HOCJ (PHOCJ), for approximating the values of American put options. The new scheme, primarily based upon the high-order compact discretization of Jain (HOCJ) and front-fixing transformation, cancels temporarily the unknown boundary-dependent terms out to derive a compact scheme first and then reconsiders them to develop the final whole valuation scheme. By doing this, we successfully eliminate the inner non-linearity introduced by front-fixing transformation in our PHOCJ scheme, thus refraining from Newton's iterations. Numerical results show that under the same parameters settings, our PHOCJ scheme keeps a higher accuracy and faster convergence rate than both CN and HOCJ scheme.