Risk Management with Options and Futures under Liquidity Risk

Managing price risk with futures contracts creates liquidity risk through marking to market. Liquidity risk matters in an imperfect capital market where interim losses on a futures position have to be financed at a borrowing rate that is higher than the risk-free rate. However, the impact of liquidity risk can be mitigated using options on futures. This paper analyzes the optimal risk management and production decisions of a risk-averse firm that faces joint price and liquidity risk and can trade derivatives in unbiased markets. Its main contribution is to provide a rationale for the use of futures and options on futures in imperfect capital markets for risk management purposes. The analytical results show that there is a hedging role for option on futures: If liquidity risk materializes, the firm sells options on futures in order to partly cover this liquidity need. The additional exposure to price risk created by the options position is partly offset by an adjustment of the futures position. Otherwise, no options are traded and the optimal futures position is a full hedge. Numerical results show that the existence of liquidity risk reduces the optimal futures hedge ratio and that options are not normally used before a liquidity need actually arises. The paper also provides comparative statics results.