Moments of the asset price for the Barndorff-Nielsen and Shephard model

In this paper, we derive closed-form formulas for moments of the asset price in the Barndorff-Nielsen and Shephard (BN–S) stochastic volatility model. We also present similar results where the market is driven by a BN–S-type stochastic process. It is shown that in both cases the results depend on the cumulant transform of the background driving Lévy process for the models. In this paper, we have also obtain various approximate expressions for the expected value of the square-root process for the shifted asset price with respect to the BN–S model.