COINTEGRATION AND SETTLEMENT OF COMMODITY FUTURES CONTRACTS

Abstract

Weekly live cattle prices in various markets would be expected to share common trends, i.e., they cannot be driven by separate nonstationarities because at some point the prices will diverge sufficiently for it to be economic to cross-ship the cattle, or at least the beef. This paper extends previous bivariate work to a multivariate analysis that is capable of modeling the multiple market linkages in prices for many geographical regions. The empirical estimation represents the application of an innovation on Aoki's Linear Systems State Space model that allows determination of long- and short-run dynamics common to multiple series. The common dynamics permit characterization of the multiple markets with a limited number of states (sufficient statistics for the past), resulting in dynamic arbitrage relations between the series. A nonparametric test is used to evaluate the value of expected arbitrage forecasts implied by the structure of the model. The arbitrage relationship also is employed to generate efficient discounts/premiums for either physical delivery or cash settlement of futures contracts. The proposed settlement mechanism accounts for spatial arbitrage opportunities and therefore better represents the true geographical discounts faced by traders in individual markets.