Mean Reversion in Stock Index Futures Markets: A Nonlinear Analysis

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. © 2002 Wiley Periodicals, Inc.