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