Likelihood estimation of Levy-driven stochastic volatility models through realized variance measures

P>This paper studies the impact of jumps and leverage-type effects on return and realized variance calculations when the logarithmic asset price is given by a stochastically scaled Levy process. Realized variance is not a consistent estimator of the integrated squared volatility process in such a modelling framework, but it can nevertheless be used within a quasi-maximum likelihood setup to draw inference on the model parameters. This paper introduces a new methodology for deriving all cumulants of the returns and of the realized variance in explicit form by solving a recursive system of inhomogeneous ordinary differential equations.