• Inference;
  • Leverage effect;
  • Lévy processes;
  • Realized variance;
  • Stochastic volatility;
  • Superposition;
  • Quasi-maximum likelihood

Summary  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 Lévy 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.