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On the Convergence of a Crank–Nicolson Fitted Finite Volume Method for Pricing American Bond Options

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  • Xiaoting Gan
  • Dengguo Xu

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.

Suggested Citation

  • Xiaoting Gan & Dengguo Xu, 2020. "On the Convergence of a Crank–Nicolson Fitted Finite Volume Method for Pricing American Bond Options," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-13, May.
    • Handle: RePEc:hin:jnlmpe:1052084
    DOI: 10.1155/2020/1052084
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    Cited by:

    1. Indu Rani & Chandan Kumar Verma, 2024. "Analyzing Short-Rate Models for Efficient Bond Option Pricing: A Review," SN Operations Research Forum, Springer, vol. 5(3), pages 1-26, September.

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