Hedging Forward Positions: Basis Risk Versus Liquidity Costs

Abstract

Consider an agent with a forward position of an illiquid asset (e.g. a commodity) that has to be closed before delivery. Suppose that the liquidity of the asset increases as the delivery date approaches. Assume further that the agent has two possibilities for hedging the risk inherent in the forward position: first, he can enter customized forward contracts; second, he can acquire standardized and liquidly traded forward contracts. We assume that purchasing customized forwards perfectly eliminates the risk, but entails high liquidity costs charged by the counterparty. The standardized forwards can be acquired at considerably lower costs, but do not perfectly match the agent's risk and hence entail basis risk. By means of stochastic control we show how to obtain an optimal trade-off between liquidity costs and basis risk. To this end we reduce the hedging problem to a family of stopping problems. In two case studies we consider simple liquidity dynamics for which optimal hedging strategies can be calculated explicitly.

Keywords: illiquidity, basis risk, optimal liquidation, hedging, singular stochastic control, optimal stopping