Accurate and efficient pricing of vanilla stock options via the Crandall-Douglas scheme.
type: Item
instance of: scholarly article
title: Accurate and efficient pricing of vanilla stock options via the Crandall-Douglas scheme.
zbMATH Open document ID: 1053.91062
DOI: 10.1016/S0096-3003(02)00343-0
author: Brian J. McCartin
author: Suzanne M. Labadie
published in: Applied Mathematics and Computation
publication date: 2003-07-30T00:00:00Z
review text: The authors present a highly efficient and accurate numerical procedure for pricing vanilla stock options. The nexus of proposed numerical approximation was the Crandall-Douglas scheme for the discretization of the diffusion operator. This scheme is fourth-order accurate and unconditionally stable. For European options, numerical simulations demonstrated its superiority over competing finite difference scheme. When applied to the variational inequality for American options, the Crandall-Douglas scheme produces a linear complementary problem to be solved at each time step. The resulting time evolution matrix has been shown to be a tridiagonal \(M\)-matrix. It is observed that the sign properties of the linear complementary problem vector \(q\) permit application of the Elliot-Ockendon scheme. Thus, each linear complementary problem which arises may be solved using only \(O(N)\) arithmetic operations. Proposed technique is second-order accurate in time, fourth-order accurate in space, involves a computational stencil of only six points, and runs in linear time.
reviewed by: Aleksandr D. Borisenko
Mathematics Subject Classification ID: 91G60
Mathematics Subject Classification ID: 91G20
zbMATH DE Number: 1957176
zbMATH Keywords: numerical procedure
zbMATH Keywords: pricing vanilla stock options
zbMATH Keywords: Crandall-Douglas scheme
zbMATH Keywords: discretization of the diffusion operator
zbMATH Keywords: fourth-order accurate
zbMATH Keywords: variational inequality
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1957176