Abstract
Abstract This paper presents an implicit method for solving PDE models of contingent claims prices with general algebraic constraints on the solution. Examples of constraints include barriers and early exercise features. In this unified framework, barrier options with or without American-style features can be handled in the same way. Either continuously or discretely monitored barriers can be accommodated, as can time-varying barriers. The underlying asset may pay out either a constant dividend yield or a discrete dollar dividend. The use of the implicit method leads to convergence in fewer time steps compared to explicit schemes. This paper also discusses extending the basic methodology to the valuation of two asset barrier options and the incorporation of automatic time stepping.
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