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

摘要

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.