Price Hedging with Local and Aggregate Quantity Risk

Abstract

The authors present a method to minimize Value–at–Risk where price, local quantity, and aggregate quantity are all stochastic and correlated. The framework is quite general in that it accommodates both local and aggregate quantity, and the quantity variable may be for an asset that is subject to a stochastic convenience yield. The framework is more general than that of Ahn et al. [1999]. The solution identifies an optimal strike price for a quantity–triggered put option used to minimize Value–at–Risk. The authors identify situations where this put option is more effective than its plain–vanilla counterpart in reducing both price and quantity risks.