Discretization of L\'evy semistationary processes with application to estimation

Understand

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.