Numerical convergence properties of option pricing PDEs with uncertain volatility |
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Authors: | Pooley D M; Forsyth P A; Vetzal K R |
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Institution: |
1 School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 2 Centre for Advanced Studies in Finance, University of Waterloo, Ontario, Canada N2L 3G1
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Abstract: | The pricing equations derived from uncertain volatility modelsin finance are often cast in the form of nonlinear partial differentialequations. Implicit timestepping leads to a set of nonlinearalgebraic equations which must be solved at each timestep. Tosolve these equations, an iterative approach is employed. Inthis paper, we prove the convergence of a particular iterativescheme for one factor uncertain volatility models. We also demonstratehow non-monotone discretization schemes (such as standard CrankNicolsontimestepping) can converge to incorrect solutions, or lead toinstability. Numerical examples are provided. |
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Keywords: | nonlinear PDE option pricing convergence viscosity solution uncertain volatility |
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