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    Convergence analysis of power penalty method for American bond option pricing

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    Authors
    Zhang, K.
    Teo, Kok Lay
    Date
    2013
    Type
    Journal Article
    
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    Citation
    Zhang, K. and Teo, K.L. 2013. Convergence analysis of power penalty method for American bond option pricing. Journal of Global Optimization. 56 (4): pp. 1313-1323.
    Source Title
    Journal of Global Optimization
    DOI
    10.1007/s10898-012-9843-1
    ISSN
    09255001
    URI
    http://hdl.handle.net/20.500.11937/8052
    Collection
    • Curtin Research Publications
    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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