Futures Replication and the Law of One Futures Price

We define a synthetic futures contract as a pair consisting of a terminal futures price [Formula: see text] (a prespecified random variable) and a zero-value trading strategy whose terminal cumulative cash flow is equal to [Formula: see text] to within an additive constant. The construction of synthetic futures contracts is demonstrated for (i) futures on futures, (ii) futures on spot, (iii) quanto futures on futures, (iv) quanto futures on spot and (v) futures on foreign futures and domestic futures. We formulate and derive the Law of One Futures Price, which justifies futures pricing based on such replication.