Optimization of the Standard Lattice Sequence for Multidimensional Integrals Regarding Large-Scale Finance Problems

Lots of challenges in the multidimensional option pricing exist since this is one of the fundamental discipline in large-scale finance problems today. In this paper, for the first time we develop some new highly accurate lattice sequences, based on component-by-component construction methods: construction of rank-1 lattice rules with prime number of points and with product weights; construction of rank-1 lattice sequences with prime number of points and with product weights; construction of polynomial rank-1 lattice sequences in base 2 and with product weights. Our methods show significantly optimization compared to the results produced by the standard Monte Carlo algorithms and the most widely used lattice sequence. There is optimization in the relative error as well as the computational complexity and number of operation necessary to compute the arisen multidimensional integrals. The obtained results will play an extremely principal multi-sided role.