Abstract
In this paper we propose a general methodology to solve partial differential inequalities arising in the valuation of financial derivatives. Firstly we show how to build up a weak formulation and how to discretize it by implicit finite difference schemes in time and finite elements in space and we propose an iterative algorithm to solve the discrete variational inequality. Although the methodology is quite general, here it is applied to solve two important two-factor models: one for valuation of dividend paying Amerasian options and another for convertible bonds with stochastic interest rate and call and put features. In both cases we validate our results with some others existing in the literature.
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