  When interest rate dynamics are described by the Libor Market Model as in
BGM97, we show how some essential risk-management results can be obtained from
the dual of the calibration program. In particular, if the objetive is to
maximize another swaption's price, we show that the optimal dual variables
describe a hedging portfolio in the sense of \cite{Avel96}. In the general
case, the local sensitivity of the covariance matrix to all market movement
scenarios can be directly computed from the optimal dual solution. We also show
how semidefinite programming can be used to manage the Gamma exposure of a
portfolio.
