  We address the Cauchy problem for a nonlinear Schr{\"o}dinger equation where
the dispersion is modulated by a deterministic noise. The noise is understood
as the derivative of a self-affine function of order H $\in$ (0, 1). Due to the
self-similarity of the noise, we obtain modified Strichartz estimates which
enables us to prove the global well-posedness of the equation for
L2-supercritical nonlinearities. This is an occurence of regularization by
noise in a purely deterministic context.
