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Nonlinear dynamics in arbitrage of the S&P 500 index and futures: A threshold error-correction model

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  • Kim, Bong-Han
  • Chun, Sun-Eae
  • Min, Hong-Ghi

Abstract

Using a three-regime threshold error-correction model, we investigate the nonlinear dynamics of the S&P 500 index and futures. First, using the SupLM statistic, we report estimates of two thresholds for the three-regime model to explain the nonlinear dynamics in arbitrage of the S&P 500 index and futures. This provides empirical evidence of the no-arbitrage band predicted by the cost-of-carry model. Second, using quasi-maximum likelihood estimation, we demonstrate that those indexes that are located outside the no-arbitrage band are a nonlinear stationary process of mean-reversion to the no-arbitrage band. However, index and futures that are located within the no-arbitrage band are non-stationary. Third, we confirm an earlier finding that futures price leads the nonlinear mean-reverting behavior of the index but not vice versa. Impulse response function analysis and forecasting performance of three-regime error-correction model reinforce our findings and our estimation results are robust with different specifications of pricing error terms and endogenous variables.

Suggested Citation

  • Kim, Bong-Han & Chun, Sun-Eae & Min, Hong-Ghi, 2010. "Nonlinear dynamics in arbitrage of the S&P 500 index and futures: A threshold error-correction model," Economic Modelling, Elsevier, vol. 27(2), pages 566-573, March.
    • Handle: RePEc:eee:ecmode:v:27:y:2010:i:2:p:566-573
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    5. Qingbin Gong & Zhe Yang, 2020. "Arbitrage, speculation and futures price fluctuations with boundedly rational and heterogeneous agents," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 15(4), pages 763-791, October.

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