  We study the optimal stopping problem of pricing an American Put option on a
Zero Coupon Bond (ZCB) in the Musiela's parametrization of the
Heath-Jarrow-Morton (HJM) model for forward interest rates.
  First we show regularity properties of the price function by probabilistic
methods. Then we find an infinite dimensional variational formulation of the
pricing problem by approximating the original optimal stopping problem by
finite dimensional ones, after a suitable smoothing of the payoff. As expected,
the first time the price of the American bond option equals the payoff is shown
to be optimal.
