A Stochastic Dynamic Program for Valuing Options on Futures

摘要

We propose a stochastic dynamic program (SDP) for valuing options on stock-index futures. SDP accommodates European- as well as American-style options, and price limits on the underlying futures contracts. Our numerical investigation shows convergence, robustness, and efficiency. SDP presents some advantages and disadvantages with respect to the binomial tree and finite differences, and stands as a viable alternative to these classic numerical methodologies for option valuation. Our empirical investigation, which focuses on American options on the S&P 500 futures contract, is almost perfect for implicit volatilities, but somewhat mitigated for historical volatilities. In volatile markets, we recommend short time windows for the volatility estimation step.