  This paper proposes swaps on two important new measures of generalized
variance, namely the maximum eigenvalue and trace of the covariance matrix of
the assets involved. We price these generalized variance swaps for
Barndorff-Nielsen and Shephard model used in financial markets. We consider
multiple assets in the portfolio for theoretical purpose and demonstrate our
approach with numerical examples taking three stocks in the portfolio. The
results obtained in this paper have important implications for the commodity
sector where such swaps would be useful for hedging risk.
