On the Convergence of a Crank–Nicolson Fitted Finite Volume Method for Pricing American Bond Options. (28th May 2020)

• Record Type: Journal Article
• Authors: Gan, Xiaoting; Xu, Dengguo
• Other Names: Mitsotakis Dimitrios Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2020(2020)
• Publication Date: 2020-05-28
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2020/1052084
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : This paper develops and analyses a Crank–Nicolson fitted finite volume method to price American options on a zero-coupon bond under the Cox–Ingersoll–Ross (CIR) model governed by a partial differential complementarity problem (PDCP). Based on a penalty approach, the PDCP results in a nonlinear partial differential equation (PDE). We then apply a fitted finite volume method for the spatial discretization along with a Crank–Nicolson time-stepping scheme for the PDE, which results in a nonlinear algebraic equation. We show that this scheme is consistent, stable, and monotone, and hence, the convergence of the numerical solution to the viscosity solution of the continuous problem is guaranteed. To solve the system of nonlinear equations effectively, an iterative algorithm is established and its convergence is proved. Numerical experiments are presented to demonstrate the accuracy, efficiency, and robustness of the new numerical method.