  The VIX call options for the Barndorff-Nielsen and Shephard models will be
discussed. Derivatives written on the VIX, which is the most popular volatility
measurement, have been traded actively very much. In this paper, we give
representations of the VIX call option price for the Barndorff-Nielsen and
Shephard models: non-Gaussian Ornstein--Uhlenbeck type stochastic volatility
models. Moreover, we provide representations of the locally risk-minimizing
strategy constructed by a combination of the underlying riskless and risky
assets. Remark that the representations obtained in this paper are efficient to
develop a numerical method using the fast Fourier transform. Thus, numerical
experiments will be implemented in the last section of this paper.
