Exercise Solution 8.10

We define a single asset, with 1S1 representing the USD value, accumulated from time 0 to time 1, of a single April gold contract. Holdings ω = 12. We obtain mapping


Futures contracts margin daily, with their market value being reset to 0 with each margin payment (keep in mind the difference between the settlement price and market value of a futures contract). Accordingly, the accumulated value 1S1 of the futures contract at time 1 will be simply the margin payment due to be received at that time. This equals the change in the contract’s settlement price between time 0 and time 1, multiplied by 100 to reflect the fact that settlement prices are quoted per ounce while each futures contract is for 100 ounces. We define a mapping


Substituting [s2] into [s1], we obtain our primary mapping: