Moments and properties of multiplicatively constrained bivariate lognormal distribution with applications to futures hedging

In this paper, we derive explicit expressions for marginal and product moments of a bivariate lognormal distribution when a multiplicative constraint is present. We show that the coefficients of variation always decrease regardless of the multiplicative constraint imposed. We also evaluate the effects of the constraint on the variances and covariance, and present conditions under which the correlation coefficient increases under the presence of such a multiplicative constraint. We finally apply these results to futures hedging analysis and some other financial applications.