Modulus-based Successive Overrelaxation Iteration Method for Pricing American Options with the Two-asset Black–Scholes and Heston's Models Based on Finite Volume Discretization

Abstract

In this paper we introduce a new numerical method for the linear complementarity problems (LCPs) arising from two-asset Black-Scholes and Heston's stochastic volatility American options pricing. Based on barycenter dual mesh, a class of finite volume method (FVM) is proposed for the spatial discretization, coupled with the backward Euler and Crank-Nicolson schemes are employed for time stepping of the partial differential equations (PDEs). Then, for the resulting time-dependent LCPs are solved by using an efficient modulus-based successive overrelaxation (MSOR) iteration method. Numerical experiments are carried out to verify the efficiency and usefulness of the proposed method.

Lattice Boltzmann method for the linear complementarity problem arising from American option pricing

“…Table 7 gives the RMS with different time steps for r = 0.1. Table 8 shows the relative errors and CPU times for the LBM, projected successive overrelaxation (PSOR) method, and modulus-based successive overrelaxation (MSOR) method [45] at r = 0.1. By comparing the above results it is shown that our proposed method has higher accuracy and takes much less CPU times.…”