Dynamic optimal hedge ratio design when price and production are stochastic with jump

Abstract

In this paper, we focus on the farmer’s risk income when using commodity futures, when price and output processes are randomly correlated and represented by jump-diffusion models. We evaluate the expected utility of the farmer’s wealth and determine the optimal consumption rate and hedging position at each point in time given the harvest timing and state variables. We find a closed form for the optimal consumption and positioning rate in the case of an investor with CARA utility. This result (see Table 3.3) is a generalization of the result of Ho (J Financ 39:351–376, 1984), which considers the special case in which price and output are diffusion models.