On the martingale framework for futures prices

We provide a framework for the martingale representation for futures prices which has some concrete advantages over the classical treatments of Duffie (Dynamic Asset Pricing Theory, 3rd Edition, Princeton University Press, Princeton, NJ, 2001) or Karatzas and Shreve (Brownian Motion and Stochastic Calculus, 2nd Edition, Springer, New York, 1997). In particular, the new formulation accommodates models where the distribution of the associated risk-free rate has unbounded support. This relaxation is particularly useful in the theory of LIBOR futures.