The authors introduce, in this paper, a method for solving nonlinear quadratic Pareto problems. The method provides the analyst with a set of time series realizations for the variables in the economy. By obtaining a large number of these realizations, they can approximate the empirical distributions of a variety of statistics, which will give a detailed description of the model's properties. In particular, those statistics can be compared with the similar ones obtained from actual data, and different criteria for goodness of fit can be defined on the basis of these comparisons.

We provide an analytical discussion of the optimal hedge ratio under discrepancies between the futures market price and its theoretical valuation according to the cost-of-carry model. Assuming a geometric Brownian motion for spot prices, we model mispricing as a specific noise component in the dynamics of futures market prices. Empirical evidence on the model is provided for the Spanish stock index futures. Ex-ante simulations with actual data reveal that hedge ratios that take into account the estimated, time varying, correlation between the common and specific disturbances, lead to using a lower number of futures contracts than under a systematic unit ratio, without generally losing hedging effectiveness, while reducing transaction costs and capital requirements. Besides, the reduction in the number of contracts can be substantial over some periods. Finally, a mean–variance expected utility function suggests that the economic benefits from an optimal hedge can be substantial.