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Implicit solution of uncertain volatility/transaction cost option pricing models with discretely observed barriers. (English) Zbl 1072.91578
Summary: Option pricing models with uncertain volatility/transaction costs give rise to a nonlinear PDE. Previous work has focused on explicit methods. However, pricing discretely observed barrier options requires a very small grid spacing near the barrier, and as a result, the maximum stable timestep for an explicit method is impractically small. A fully implicit method is developed for nonlinear option pricing models, and applied to arithmetic step options, where the option loses a fraction of its value for every day over the barrier.

MSC:
91G60 Numerical methods (including Monte Carlo methods)
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
91G20 Derivative securities (option pricing, hedging, etc.)
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