Efficient pricing of Asian options under Lévy processes based on Fourier cosine expansions. Part II. Early-exercise features and GPU implementation

In this article, we propose an efficient pricing method for Asian options with early–exercise features. It is based on a two–dimensional integration and a backward recursion of the Fourier coefficients, in which several numerical techniques, like Fourier cosine expansions, Clenshaw–Curtis quadrature and the Fast Fourier transform (FFT) are...

Saddlepoint Approximations for Expectations and an Application to CDO Pricing

We derive two types of saddlepoint approximations for expectations in the form of E[(X - K)+], where X is the sum of n independent random variables and K is a known constant. We establish error convergence rates for both types of approximations in the independently and identically distributed case. The approximations are further extended to...

Improving multigrid for 3-D electro-magnetic diffusion on stretched grids

We evaluated multigrid techniques for 3D diffusive electromagnetism. The Maxwell equations and Ohm's law were discretised on stretched grids, with stretching in all coordinate directions. We compared standard multigrid to alternative multigrid approaches with linewise smoothing and semi-coarsening, both as a stand-alone solver and as a...