We propose a stochastic dynamic program for valuing options on stock-index futures. The model accounts for deterministic, seasonally varying dividends generated by stock indices, although they do not intervene in our numerical procedure. Our methodology accommodates European- as well as American-style options, and price limits on the underlying futures contracts. We solve the model, and run the program for valuing options on S&P 500 futures, traded on the Chicago Mercantile Exchange. Our approach presents several advantages, and competes very well with binomial trees, finite differences, and ad-hoc numerical procedures. Our numerical and empirical investigation demonstrates convergence, robustness, efficiency, and consistency.