  Motivated by the construction of the It\^o stochastic integral, we consider a
step function method to discretize and simulate volatility modulated L\'evy
semistationary processes. Moreover, we assess the accuracy of the method with a
particular focus on integrating kernels with a singularity at the origin. Using
the simulation method, we study the finite sample properties of some recently
developed estimators of realized volatility and associated parametric
estimators for Brownian semistationary processes. Although the theoretical
properties of these estimators have been established under high frequency
asymptotics, it turns out that the estimators perform well also in a low
frequency setting.
