A Front-Fixing Based HOC Scheme for Pricing American Options with a High-Order Treatment to the Boundary

摘要

We enhance D.Y.Tangman et.al's work(D.Y.Tangman,A.Gopaul,M.Bhuruth.2008.“Numerical pricing of options using high-order compact finite difference schemes,” Journal of Computational and Applied Mathematics,218:270-280)by employing a high-order treatment to the optimal exercise boundary.In our approach,both two-and three-order finite difference methods are used to approximate the fictitious points assumed to equal the transformed payoff function in D.Y.Tangman et.al's,respectively.Besides,the Newton's iteration is only applied to solve the boundary,thus reducing significantly the complexity of deriving the HOCJ scheme while keeping the accuracy.Numerical experiments shows that our approaches have a higher accuracy and faster convergence than D.Y.Tangman's.