Optimal futures hedging strategies based on an improved kernel density estimation method

In this paper, we study the hedging effectiveness of crude oil futures on the basis of the lower partial moments (LPMs). An improved kernel density estimation method is proposed to estimate the optimal hedge ratio. We investigate crude oil price hedging by contributing to the literature in the following twofold: First, unlike the existing studies which focus on univariate kernel density method, we use bivariate kernel density to calculate the estimated LPMs, wherein the two bandwidths of the bivariate kernel density are not limited to the same, which is our main innovation point. According to the criterion of minimizing the mean integrated square error, we derive the conditions that the optimal bandwidths satisfy. In the process of derivation, we make a distribution assumption locally in order to simplify calculation, but this type of local distribution assumption is far better than global distribution assumption used in parameter method theoretically and empirically. Second, in order to meet the requirement of bivariate kernel density for independent random variables, we adopt ARCH models to obtain the independent noises with related to the returns of crude oil spot and futures. Genetic algorithm is used to tune the parameters that maximize quasi-likelihood. Empirical results reveal that, at first, the hedging strategy based on the improved kernel density estimation method is of highly efficiency, and then it achieves better performance than the hedging strategy based on the traditional parametric method. We also compare the risk control effectiveness of static hedge ratio vs. time-varying hedge ratio and find that static hedging has a better performance than time-varying hedging.