  We derive representations of local risk-minimization of call and put options
for Barndorff-Nielsen and Shephard models: jump type stochastic volatility
models whose squared volatility process is given by a non-Gaussian
rnstein-Uhlenbeck process. The general form of Barndorff-Nielsen and Shephard
models includes two parameters: volatility risk premium $\beta$ and leverage
effect $\rho$. Arai and Suzuki (2015, arxiv:1503.08589) dealt with the same
problem under constraint $\beta=-\frac{1}{2}$. In this paper, we relax the
restriction on $\beta$; and restrict $\rho$ to $0$ instead. We introduce a
Malliavin calculus under the minimal martingale measure to solve the problem.
