Mean reversion in stock index futures markets: A nonlinear analysis

Abstract

Several stylized theoretical models of futures basis behavior under nonzero transactions costs predict nonlinear mean reversion of the futures basis towards its equilibrium value. Nonlinearly mean-reverting models are employed to characterize the basis of the S&P 500 and the FTSE 100 indices over the post-1987 crash period, capturing empirically these theoretical predictions and examining the view that the degree of mean reversion in the basis is a function of the size of the deviation from equilibrium. The estimated half lives of basis shocks, obtained using Monte Carlo integration methods, suggest that for smaller shocks to the basis level the basis displays substantial persistence, while for larger shocks the basis exhibits highly nonlinear mean reversion towards its equilibrium value.

Unit Root Tests for ESTAR Models

“…This de-mean strategy was also applied in He and Sandberg (2005). Empirical examples in Venetis et al (2009) and Monoyios and Sarno (2002) support the assumption is satisfied in practice.…”

“…Terasvirta and Elliasson (2001), and Sarno et al (2002) used ESTAR models to analyse deviations from optimal money holding. Monoyios and Sarno (2002) found that symmetric deviations from arbitrage processes such as stock index futures follow ESTAR models. In economics and finance theories such as real exchange rate, PPP, and arbitrage processes, ESTAR models can be characterised by a unit root behaviour in the inner regime, but for large deviations, the process is mean reverting.…”