Efficient conservative second-order central-upwind schemes for option-pricing problems

摘要

The conservative Kurganov-Tadmor (KT) scheme has been successfully applied to option-pricing problems by German I. Ramirez-Espinoza and Matthias Ehrhardt. These included the valuation of European, Asian and nonlinear options as Black-Scholes partial differential equations, written in the conservative form, by simply updating fluxes in the black box approach. In this paper, we describe an improvement of this idea through a fully vectorized algorithm of nonoscillatory slope limiters and the efficient use of time solvers. We also propose the application of second-order extensions of KT to option-pricing problems. Our test problems solve one-dimensional benchmark and convection-dominated European options as well as digital and butterfly options. These demonstrate the robustness and flexibility of the pricing methods and set a basis for complex problems. Further, the computation of option Greeks ensures the reliability of these methods. Numerical experiments are performed on barrier options, early exercisable American options and two-dimensional fixed and floating strike Asian options. To the authors' knowledge, this is the first time American options have been priced by applying the early exercise condition on the semi-discrete formulation of central-upwind schemes. Our results show second-order, nonoscillatory and high-resolution properties of the schemes as well as computational efficiency.