Index Arbitrage and Nonlinear dynamics Between the S&P 500 Futures and Cash

Abstract

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Mean reversion in stock index futures markets: A nonlinear analysis

“…10 One notable example in the literature of a study proposing asymmetries is due to Brennan and Schwartz (1990), who suggest that if the transactions costs of arbitrage are asymmetric and arbitrage affects the level of the basis then such asymmetry is likely to be reflected in the distribution of the basis. Nevertheless, in general, there is fairly convincing evidence that the distribution of the basis is symmetric-notably, see the evidence provided by Dwyer et al (1996) using both parametric and nonparametric tests of symmetry applied to data for the S&P 500 index.…”

“…For example, Chan (1992), Dwyer et al (1996), and Miller et al (1994) have used 5-, 15-, and 5-min intervals, respectively. 13 For an application of nonlinear models to higher frequency data in this context, see Taylor, van Dijk, Franses, and Lucas (2000).…”

“…Consequently, one might expect that allowing for nonlinear adjustment toward equilibrium in the empirical modeling of the futures basis may yield a more satisfactory approximation to the true unknown data generating process driving the basis, improving upon linear specifications. 1 See, e.g., Dwyer, Locke, and Yu (1996), Martens, Kofman, and Vorst (1988), and Yadav, Pope, and Paudyal (1994). See also Lo and MacKinlay (1999, Chap.…”

“…Section 5 reports the results of summary statistics and univariate unit root tests applied to basis data, cointegration tests applied to a regression involving the spot price and the futures price, linearity tests applied to the basis data, and the estimation results from employing nonlinear models to characterize the basis of the S&P 500 and the FTSE 100 indices. In Section 6 Monte Carlo integration methods are used to calculate the half-lives implied by estimated nonlinear models for the basis, further examining how the nonlinear estimation results can improve the profession's understanding of the dynamics 2 The literature related to the present study is very large and includes, among others, Blank (1991), Brennan and Schwartz (1990), Chan (1992), Dwyer et al (1996), Figlewski (1984), Mougoue (1997a, 1997b), Gao and Wang (1999), Kawaller (1991), Kawaller, Koch, and Koch (1987), Klemkosky and Lee (1991), Lekkos and Milas (2001), Ramaswamy (1988), Miller, Muthuswamy, andWhaley (1994), Modest and Sundaresan (1983), Parhizgari and de Boyrie (1997), Sarno and Valente (2000), Stoll and Whaley (1990), Brorsen (1993, 1994), Yadav et al (1994). 3 See, e.g., Dumas (1994) and Sofianos (1993) on this point.…”

“…These threshold models allow for a transactions costs band within which no adjustment takes place-so that deviations from the basis may exhibit unit root behavior-while outside the band the process switches abruptly to become stationary autoregressive. Studies using threshold models provide evidence against linearity in the deviation of the basis from its equilibrium level and in favor of threshold-type behavior (e.g., Yadav et al, 1994;Dwyer et al, 1996;Martens et al, 1998).…”