An Alternative Formulation for the Pricing of Stock Index Futures: Theoretical and Empirical Perspectives

Abstract

Assuming that a futures price is a function of the underlying asset and the basis, and that a Brownian bridge process drives the basis, this article provides the closed-form solution of futures with basis risk (FBR). The Brownian bridge process ensures that the basis is zero at the maturity of a futures contract. The FBR model is empirically tested with daily S&P500 futures data and is found to outperform both the Cornell and French (CF,1983a) and Yan (2002) models. The overall mean errors in terms of index points and_x000D_ percentages are 0.1918 and −0.002% for the FBR model, compared to −1.8806 and −0.2088% for the CF model, and 2.5072 and 0.0973% for the Yan model.