Determine the efficiency of Numerical integration

Question

Determine the efficiency of Numerical integration?

Answer 1

There are several numerical quadrature methods. But the two most common are based on random number generation again. One uses normally distributed numbers and the other uses what are termed as low-discrepancy sequences. The low-discrepancy numbers are clever in which they appear superficially to be random but don't contain the inevitable clustering that truly random numbers have.

Using the easiest normal numbers, if you need an accuracy of ε and you are pricing M options the time occupied will be O(Mε^-2).

If you utilize the low-discrepancy numbers the time occupied will be O(Mε^-1).

You can notice that this method is very fast, unfortunately this isn't frequently applicable.