A more informative estimation procedure for the parameters of a diffusion process

The estimation procedures for the parameters of a diffusion process with constant coefficients have mainly focused on volatility. Nevertheless, even if the knowledge of the volatility alone suffices to compute the Black and Scholes option prices, other financial application models assume that the price dynamics follows a log-normal process and requires the knowledge of both parameters. On the other hand, while the usual ML estimator of volatility gives satisfactory results, the estimation of drift is much less accurate; moreover, the drift-estimated value highly depends on the phases of the business cycle included in the sample data. This contribution explicitly imposes a risk aversion or risk neutral assumption into the ML estimation procedure and makes a constrained maximization of the sample likelihood function. The aim is twofold: to obtain estimated values which are consistent with a widely accepted assumption and use the risk aversion constraint in order to improve the accuracy of the estimates.