Abstract
A set of elementary axioms for stochastic finance is presented wherein a prominent role is played by the state-price density, which in turn determines the stochastic dynamics of the interest-rate term structure. The fact that the state-price density is a potential implies the existence of an asymptotic random variable X∞ with the property that its conditional variance is the state-price density. The Wiener chaos expansion technique can then be applied to X∞, thus enabling us to 'parametrize' the dynamics of the discount-bond system in terms of the deterministic coefficients of the chaos expansion. Using this method, we find that there is a natural map from the space of all admissible term-structure trajectories to the symmetric Fock space F naturally associated with the space of square-integrable random variables on the underlying probability space. An element of F is either coherent or incoherent, and a stochastic bond-price system is necessarily represented by an incoherent element of F. Making use of the linearity of F we derive simple analytic formulae for the bond-price system, the volatility structure, the short rate, and the risk premium associated with an arbitrary admissible term-structure model. Extensions to foreign-exchange markets and general asset systems are also developed.