In a perfectly efficient market, after adjusting for drift, futures prices would follow a martingale model. The martingale property implies that the changes in futures prices should be serially uncorrelated. This study finds that the price changes of the S&P 500 futures contracts during 1983 and 1984 have negative serial correlation and are better described by a random walk model with reflecting barriers or by a random walk model with reflecting barriers and mean reversion.

This paper presents a unified method for closed-form pricing of European options on assets with diffusion prices. The method uses linear and nonlinear time and scale changes to reduce complex diffusion processes to known processes, thereby generating option pricing formulas for new diffusion processes and unifying existing results. Applications include: systematically modelling the effects on option prices of time-dependent variability in the underlying asset price, valuing futures options and options on assets showing maturity-related or seasonal volatility, valuing options on new nonconstant elasticity-of-variance diffusion processes, and pricing generalized options.

This paper derives and numerically simulates maximum likelihood estimators for the drift in several important diffusion price models. The time series convergence properties of these estimators are compared to those of standard estimators including the geometric and arithmetic means. Merton (1980) demonstrated that it is difficult to efficiently estimate the drift in a log-normal diffusion model. We qualify and strengthen his result by noting that his estimator is the maximum likelihood estimator and by applying our simulation results. However, we also demonstrate that it is possible to efficiently estimate the drift in other useful diffusion price models. In particular, by asking just how much time is needed in order for the maximum likelihood estimators of the drift in different diffusion processes to converge, these results qualify and quantify Black's (1993) statement that “we need such a long period to estimate the average that we have little hope of seeing changes in expected return."