The pricing of futures contracts and the arbitrage pricing theory

When interest rates are stochastic, the cash flows of futures and forward contracts differ because of the marking‐to‐market requirement of futures contracts. The price effect of this difference is examined here by applying the risk and return model of the arbitrage pricing theory. The resulting futures pricing equation is preference free, and is obtainable using other no‐arbitrage approaches. The pricing equation suggests that the price difference is due to the covariance of spot asset returns and interest rates. An empirical study is conducted on the Major Market Index futures from October 1, 1984 to September 27, 1985. Results indicate that the covariance, extracted by the Kalman filter according to the pricing equation, is significant in the pricing of futures contracts.