Index arbitrage and nonlinear dynamics between the S&P 500 futures and cash

We use a cost of carry model with nonzero transactions costs to motivate estimation of a nonlinear dynamic relationship between the S&P 500 futures and cash indexes. Discontinuous arbitrage suggests that a threshold error correction mechanism may characterize many aspects of the relationship between the futures and cash indexes. We use minute-by-minute data on the S&P 500 futures and cash indexes. The results indicate that nonlinear dynamics are important and related to arbitrage and suggest that arbitrage is associated with more rapid convergence of the basis to the cost of carry than would be indicated by a linear model.