Convergence analysis of power penalty method for American bond option pricing

Convergence analysis of power penalty method for American bond option pricing

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Article ID: iaor20134054
Volume: 56
Issue: 4
Start Page Number: 1313
End Page Number: 1323
Publication Date: Aug 2013
Journal: Journal of Global Optimization
Authors: ,
Keywords: option pricing, global convergence
Abstract:

This paper is concerned with the convergence analysis of power penalty method to pricing American options on discount bond, where the single factor Cox–Ingrosll–Ross model is adopted for the short interest rate. The valuation of American bond option is usually formulated as a partial differential complementarity problem. We first develop a power penalty method to solve this partial differential complementarity problem, which produces a nonlinear degenerated parabolic PDE. Within the framework of variational inequalities, the solvability and convergence properties of this penalty approach are explored in a proper infinite dimensional space. Moreover, a sharp rate of convergence of the power penalty method is obtained. Finally, we show that the power penalty approach is monotonically convergent with the penalty parameter.

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