Accurate and efficient pricing of vanilla stock options via the Crandall-Douglas scheme.
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.
discretization of the diffusion operator
scientific article; zbMATH DE number 1957176
scientific article