Galerkin Infinite Element Approximation for Pricing Barrier Options and Options with Discontinuous Payoff

We analyse the Galerkin Infinite Element method for pricing European barrier options and, more generally, options with discontinuous payoff. The Infinite Element method is a very simple and efficient modification of the more common Finite Element method. It keeps the best features of Finite Elements, i.e. bandedness, easiness of programming, accuracy. Three main aspects are considered: (i) the degeneracy of the pricing PDE models at hand; (ii) the presence of discontinuities at the barriers or in the payoff clause and their effects on the numerical approximation process; (iii) the need for resorting to suitable numerical methods for unbounded domains when appropriate asymptotic conditions are not specified. The numerical stability and convergence of the proposed method are proved