Pricing American bond options using a cubic spline collocation method

Author:

El hajaji Abdelmajid,Hilal Khalid,Serghini Abdelhafid,Mermri El bekkey

Abstract

In this paper, American options on a discount bond are priced under the Cox-Ingrosll-Ross (CIR) model. The linear complementarity problem of the option value is solved numerically by a penalty method. The problem is transformed into a nonlinear partial differential equation (PDE) by adding a power penalty term. The solution of the penalized problem converges to the one of the original problem. To numerically solve this nonlinear PDE, we use the horizontal method of lines to discretize the temporal variable and the spatial variable by means of trapezoidal method and a cubic spline collocation method, respectively. We show that this full discretization scheme is second order convergent, and hence the convergence of the numerical solution to the viscosity solution of the continuous problem is guaranteed. Numerical results are presented and compared with other collocation methods given in the literature.

Publisher

Sociedade Paranaense de Matematica

Subject

General Mathematics

Cited by 6 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Lattice Boltzmann method for the linear complementarity problem arising from American option pricing;Journal of Physics A: Mathematical and Theoretical;2024-07-11

2. Projection and Contraction Method for Pricing American Bond Options;Mathematics;2023-11-18

3. A Quintic Spline Collocation Method for Solving Time-Dependent Convection-Diffusion Problems;Tatra Mountains Mathematical Publications;2021-12-01

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