Adaptive integration for multi-factor portfolio credit loss models

Multi-asset option pricing using a parallel Fourier-based technique

Computation of VaR and VaR Contribution in the Vasicek portfolio credit loss model: A comparative study

Multigrid for high dimensional elliptic partial differential equations on non-equidistant grids

This work presents techniques, theory and numbers for multigrid in a general d-dimensional setting. The main focus is the multigrid convergence for high-dimensional partial differential equations (PDEs). As a model problem we have chosen the anisotropic diffusion equation, on a unit hypercube. We present some techniques for building the general...

Higher order saddlepoint approximations in the Vasicek portfolio credit loss model

This paper utilizes the saddlepoint approximation as an efficient tool to estimate the portfolio credit loss distribution in the Vasicek model. Value at Risk (VaR), the risk measure chosen in the Basel II Accord for the evaluation of capital requirement, can then be found by inverting the loss distribution. VaR Contribution (VaRC), Expected...

On coordinate transformation and grid stretching for sparse grid pricing of basket options

We evaluate two coordinate transformation techniques in combination with a coordinate stretching for pricing basket options in a sparse grid setting. The sparse grid technique is a basic technique for solving a high-dimensional partial differential equation. By creating a small hypercube sub-grid in the 'composite' sparse grid we can also...

A novel multigrid based preconditioner for heterogeneous Helmholtz problems

An iterative solution method, in the form of a preconditioner for a Krylov subspace method, is presented for the Helmholtz equation. The preconditioner is based on a Helmholtz type differential operator with a complex term. A multigrid iteration is used for approximately inverting the preconditioner. The choice of multigrid components for the...

On a class of preconditioners for solving the Helmholtz equation

On the robustness of a Multiple Semi-coarsened Grid method

Multigrid schemes for time-dependent incompressible Navier-Stokes equations

A robust multigrid method for a discretization of the incompressible Navier-Stokes equations in general coordinates

Steady incompressible flow around objects in general coordinates with a multigrid solution method

A multigrid method for an invariant formulation of the incompressible Navier-Stokes equations in general coordinates

A multigrid method for a discretization of the incompressible Navier-Stokes equations in general coordinates