The Term Structure of Interest Rates as a Random Field

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Abstract
Note: This abstract was revised by the author since June 1997. Forward rate dynamics are modeled as a random field. In contrast to multi-factor models, random field models offer a parsimonious description of term structure dynamics, while eliminating the self-inconsistent practice of recalibration. The form of the drift of the instantaneous forward rate process necessary to preclude arbitrage under the risk neutral measure is obtained. Forward measures are characterized, and used to price a bond option when the forward volatility structure depends upon the square root of the current spot rate. In addition, it is demonstrated that random field models offer a parsimonious method to account for parameter uncertainty, inherently predicting that the best hedging instrument for a given asset is one of similar maturity. Finally, a random field is shown to be supported within a general equilibrium framework, allowing the risk-neutral measure and risk premia to be identified.