ABSTRACT
The term structure of interest rates is modeled as a random field, which has implications in both the original measure (optimal portfolio choice, hedging) and equivalent martingale measures (pricing derivative assets). Advantages to modeling term structure dynamics as a random field include:

1. The model naturally accounts for the fact that the best hedging instrument for a bond is one of similar maturity.
2. It is unnecessary to specify the number of factors that drive the term structure when pricing derivative assets.
3. The approach can mimic accounting for uncertainty in volatility estimates.

The form of the drift of the instantaneous forward rate process necessary to preclude arbitrage under the risk neutral measure is obtained. This result generalizes the work of Kennedy (1994), whose scope is limited to Gaussian random fields. The forward risk adjusted measure is characterized, and used to price a bond option when the forward volatility structure depends upon the square root of the current spot rate. A random field is shown to be supported within a general equilibrium framework for an economy whose market is made complete by introducing a continuum of bonds. Empirical advantages to modeling term structure dynamics as a random field are discussed.

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