  We propose a formulation of the term structure of interest rates in which the
forward curve is seen as the deformation of a string. We derive the general
condition that the partial differential equations governing the motion of such
string must obey in order to account for the condition of absence of arbitrage
opportunities. This condition takes a form similar to a fluctuation-dissipation
theorem, albeit on the same quantity (the forward rate), linking the bias to
the covariance of variation fluctuations. We provide the general structure of
the models that obey this constraint in the framework of stochastic partial
(possibly non-linear) differential equations. We derive the general solution
for the pricing and hedging of interest rate derivatives within this framework,
albeit for the linear case (we also provide in the appendix a simple and
intuitive derivation of the standard European option problem). We also show how
the ``string'' formulation simplifies into a standard N-factor model under a
Galerkin approximation.
