A while ago, I have applied a relatively simple adaptive Filon quadrature to the problem of volatility swap pricing. The Filon quadrature is an old quadrature from 1928 that allows to integrate oscillatory integrand like $$f(x)\cos(k x)$$ or $$f(x)\sin(k x)$$. It turns out that combined with an adaptive Simpson like method, it has many advantages over more generic adaptive quadrature methods like Gauss-Lobatto, which is often used on similar problems.