IA commodity futures swap is a portfolio of forward contracts on commodity futures. Commodity futures belong to the category of average forward contracts. Due to the linearity with respect to underlying asset prices, an average forward contract is just a linear combination of ordinary forward contracts.
The specialities of a commodity future which is matured or settled at a time T are the following. With a specified set of average time points for the commodity futures, the payoff at the maturity or the settlement date T is given by an arithmetic average of values (or prices) of assets. Such a contract is called the nearest futures related to ti. To be more precise, we denote the value of the nearest futures by Fcomm(ti; I(ti)) where I(ti) is the index of the nearest futures contract related to ti. The average is weighted by time. It should be noted that different ti and tj may be related to the same nearest futures, i.e., I(ti) may be identical to I(tj).
Let us consider crude oil as an example of commodity. In the crude oil exchange market, futures contracts are available for each calendar month. The roll over dates for MAY-99 and JUN-99 futures contracts are 20-Apr-99 and 20-May-99, respectively. If t1 = 15-Apr-99, t2 = 20-Apr-99 and t3 = 21-May-99, Then the nearest futures for t1 and t2 is the MAY-99 contract, i.e., I(t1) = I(t2) = MAY-99, and the nearest futures for t3 is the JUN-99 contract, i.e., I(t3) = JUN-99.
It is known that the value of a futures contract at a time t is equal to the futures price at that time. If without any confusion, we may also use the notation Fcomm(t; I(ti)) to represent the commodity futures price at time t of the nearest futures corresponding to time ti. Commodity futures prices are quoted as the number of units of a currency per unit amount of a commodity.
Let us denote C be a quoted cash currency in the commodity market. In the above, dimensions of the commodity price, the strike are the same, i.e., [unit of C/unit of the commodity]. The dimension of he value of the FCCF is [unit of C]. However, in some general cases, there may be more than one currencies involved: one for measuring the value of an FCCF, the second for defining a strike (or equivalently a notional principal) and the third for quoting the commodity futures prices
References: