Efficiency and Options on the Market Index

In a static exchange economy, when all the endowments are issued as securities on a stock exchange, Pareto optimal allocations may be reached by trading options on the market index (see Breeden and Litzenberger (1978)). We extend this result when some of the risks cannot be exchanged on the market. Options on an appropriate index, which typically differs from the market index, depending on the correlation of the non-tradable risks with the exchanged securities, are still an appropriate tool to support a (constrained) efficient equilibrium. This suggests that the recent development of derivatives based on interest rates may be an efficient way to reach a Pareto optimal allocation of risks