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A jump-diffusion model for a single-asset market is considered. Under this assumption the value of a European contingency claim satisfies a general partial integro-differential equation (PIDE). The equation is localized and discretized in space using finite differences and finite elements and in time by the second order backward differentiation formula(More)
Here we develop an option pricing method for European options based on the Fourier-cosine series, and call it the COS method. The key insight is in the close relation of the characteristic function with the series coefficients of the Fourier-cosine expansion of the density function. In most cases, the convergence rate of the COS method is exponential and(More)
We discuss a nonlinear multigrid method for a linear complementarity problem. The convergence is improved by a recombination of iterants. The problem under consideration deals with option pricing from mathematical finance. Linear complementarity problems arise from so-called American-style options. A 2D convection-diffusion type operator is discretized with(More)
We present a pricing method based on Fourier-cosine expansions for early-exercise and discretely-monitored barrier options. The method works well for exponential Lévy asset price models. The error convergence is exponential for processes characterized by very smooth (C ∞ [a, b] ∈ R) transitional probability density functions. The computational complexity is(More)
In this paper we try to achieve h-independent convergence with preconditioned for two-dimensional (2D) singularly perturbed equations. Three recently developed multigrid methods are adopted as a pre-conditioner. They are also used as solution methods in order to compare the performance of the methods as solvers and as preconditioners. Two of the multigrid(More)
We investigate the parallel performance of an iterative solver for 3D heterogeneous Helmholtz problems related to applications in seismic wave propagation. For large 3D problems, the computation is no longer feasible on a single processor , and the memory requirements increase rapidly. Therefore, parallelization of the solver is needed. We employ a complex(More)
This paper deals with the combination of two solution methods: multigrid and GMRES [SIAM The generality and parallelizability of this combination are established by applying it to systems of nonlinear PDEs. As the " preconditioner " for a nonlinear Krylov subspace method, we use the full approximation storage (FAS) scheme [Math. a nonlinear multigrid(More)