Galerkin infinite element approximation for pricing barrier options and options with discontinuous payoff. (English) Zbl 1106.91035
Summary: We analyze the Galerkin infinite element method for pricing European barrier options and, more generally, options with discontinuous payoff. The infinite element method is a simple and efficient modification of the more common finite element method. It keeps the best features of finite elements, i.e., bandedness, ease 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.
MSC:
| 91B28 | Finance etc. (MSC2000) |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65J10 | Numerical solutions to equations with linear operators |
Keywords:
infinite element method; pricing; European barrier options; options with discontinuous payoffReferences:
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