| This research focuses on the non-linearity in the dynamic relationship between the S&P 500 stock index futures and cash prices induced by index arbitrage. Finding that futures and cash prices are cointegrated, the Engle-Granger error correction mechanism (ECM) model is applied for this analysis.;A self-exciting threshold autoregression (SETAR) is applied to identify the transaction costs bounds associated with arbitrage. Based on the "cost of carry" model, the basis is used as the threshold variable. This part of the research consists of two stages. The results from the first stage indicate strong evidence in support of the SETAR model. The estimating method for the SETAR model is improved in the second stage. Autoregressive conditional heteroscadesticity (ARCH) is tested and corrected in the second stage estimate. The estimated thresholds are consistent with the transaction costs ratio associated with index arbitrage. Test statistics generated by Monte Carlo sampling reveal that the estimates are significant even with ARCH corrected.;With thresholds identified, the ECM model is estimated in three regimes for all the nearby contracts in 1989 and 1990. The dynamic pattern across regimes is analyzed by transferring the simultaneous higher order ECM form into a first order vector difference equation in state space. The time path of the basis, change in the futures price, and change in the cash price are investigated by generating a shock from futures and cash markets respectively. The responses of the three variables in the two tail regimes are clearly different from that in the middle regime and their behavior is consistent with the impact of arbitrage trading. The method developed in this research improves the estimate on the impact of arbitrage trading and it also offers a possibility to identify threshold phenomenon in other economic analysis. |
