Before revision:   Arai and Suzuki (2015) obtained a formula of locally risk-minimizing for L\'evy markets under many additional conditions by using Malliavin calculus for L\'evy processes. In this paper, supposing mild conditions, we make sure that the Barndorff-Nielsen and Shephard models satisfy all the conditions imposed in Arai and Suzuki (2015).
After revision:  Arai and Suzuki (2015) obtained a formula of locally risk-minimizing for L\'evy markets under many additional conditions . Supposing mild conditions, we make sure that the Barndorff-Nielsen and Shephard models satisfy all the conditions imposed in Arai and Suzuki (2015).