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

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 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.