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>Power penalty method for a linear complementarity problem arising from American option valuation
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Power penalty method for a linear complementarity problem arising from American option valuation
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机译:美国期权估值引起的线性互补问题的幂罚方法
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摘要
In this paper, we present a power penalty function approach to the linear complementarity problem arising from pricing American options. The problem is first reformulated as a variational inequality problem; the resulting variational inequality problem is then transformed into a nonlinear parabolic partial differential equation (PDE) by adding a power penalty term. It is shown that the solution to the penalized equation converges to that of the variational inequality problem with an arbitrary order. This arbitrary-order convergence rate allows us to achieve the required accuracy of the solution with a small penalty parameter. A numerical scheme for solving the penalized nonlinear PDE is also proposed. Numerical results are given to illustrate the theoretical findings and to show the effectiveness and usefulness of the method.
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