Robust Benchmark Design

Recent scandals over the manipulation of LIBOR and foreign exchange benchmarks have spurred policy discussions of the appropriate design of financial benchmarks. We solve a version of the problem faced by a financial benchmark administrator. Acting as a mechanism designer, the benchmark administrator constructs a "fixing," meaning an estimator of a market value or reference rate based on transactions or other submission data. The data are generated by agents whose profits depend on the realization of the estimator (the benchmark fixing). Agents can misreport, or trade at distorted prices, in order to manipulate the fixing. We characterize the best linear unbiased benchmark fixing.