quilibrium price processes in frictionless markets have been characterized in E a number of ways. Under risk neutrality, Samuelson (1965) first demonstrated the martingale property. Under risk aversion, one can present models in which the martingale property holds and models in which it does not (Lucas, 1978). The sample paths, or realizations, of stochastic continuous price processes must be of unbounded variation over every finite time interval: otherwise arbitrage opportunities would exist in continuous trading, frictionless markets (Harrison, Pitbladdo, and Schaefer, 1984). The unbounded variation property means that the cumulative sum of the absolute values of price changes is infinite over any finite interval of time. Price paths have infinite length over finite time intervals because unbounded variation implies that prices have infinite velocity at almost each instant of time. While the assumption of continuous sample paths is plausible, at least in a limiting sense, that of unbounded variation is not when one turns to markets which may be approximated as continuous trading markas with frictional elements.
The purpose of this article is to consider a class of continuous sample path stochastic processes which may be useful for modeling futures prices in markets with frictions. Such markets generate market prices which differ from their underlying equilibrium counterparts. It is suggested that the stochastic processes appropriate for modeling market prices also differ from the usual diffusion models useful for modeling equilibrium price processes.
Empirical futures price change series fail to exhibit the zero first order serial correlation coefficient predicted for them by equilibrium price models in frictionless markets. A number of factors contribute to this empirical finding. These include the existence of transactions costs in the form of a bid-asked spread, less than instantaneous responses to the arrival of costly new information, and imperfect costly arbitraging. With regard to the last, it has been argued by Grossman and Stiglitz (1980) that markets cannot be perfectly arbitraged at all instants of time when information is costly. Hence, empirical price series will not, in general, be perfectly arbitraged martingales. The further institutional constraint of exchangeimposed price limits will also negate the martingale property.
In Section I, futures prices are considered in a continuous time model with continuous trading and continuous settlement of futures contracts. However, the