Implicit solution of uncertain volatility/transaction cost option pricing models with discretely observed barriers Original Research Article

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.