Price-flow contract

We assume the upstream tier designs the price-flow contract, shown in the equation (1), below which is a mechanism describing the correspondence between the acquisition prices offered by downstream sites and the flow amount supplied by the upstream sites to its subsequent downstream sites. The material... 

The downstream tier determines the equilibrium prices to acquire the recycled items from its preceding upstream tier. We refer to the price-flow contract as the flow function. We assume that the transportation cost for the shipment of the recycled item between any two tiers is paid by the downstream tier entity. The price the downstream tier entity pays for transportation is taken into account by the... 

In the decentralized decision-making framework, each entity within the RPS concentrates on optimizing its own profit subject to its own transportation and processing capacity constraints. The upstream entities in one tier provide the price-flow contract that connects the downstream price information to the flow they will provide. We refer to this price-flow contract as the flow function. Each upstream entity acts individually to determine the flow function used to contract with each member of the next tier. The flow function is determined using a robust optimization formulation that captures the idea that the upstream entity does not have exact price information from the downstream entities, and wants to minimize the worst outcome it can have. 

Extreme temperatures and other weather events have become major determinants of short-term trade flows and prices on both sides of the Atlantic - but especially in North America - and will affect short-term production and demand unpredictably. Gas prices on both sides of the Atlantic have appeared to fluctuate in a band where the floor is set in the summer by the heavy (residual) fuel oil price and the ceiling in the winter by the gasoil price. For Europe, this band is roughly determined by the indexation of long-term gas contracts. In the US, it appears to be set by... 

This may lead one to ask the question of which analysis should be performed. There is no correct answer. However, as these examples illustrated, more complicated cash flow scentuios generally lead to actual dollar cash flow analysis. This is because the computation of one s tax liability is based on actual dollar cash flows. Also, contracted prices, such as loans and lease agreements, are based on actual dollar cash flows. In these situations, actual dollar cash flow analysis may be more stiaight-forward because most of the data are also in the correct form. 

Say an investor at time t simultaneously buys one unit of a zero-coupon bond maturing at time T that is priced at P t, T) and sells P t, T) P t, T + 1) units of zero-coupon bonds maturing at T+ 1. Together these two transactions generate a zero cash flow The investor receives a cash flow equal to one unit at time Tand pays out P t, T)IP t, T+ 1) at time 7+ 1. These cash flows are identical to those that would be generated by a loan contracted at time t for the period T to T + 1 at an interest rate of P t, T) P t, T + ). Therefore P t, T) P t, T+ 1) is the forward rate. This is expressed formally in (3.25). 

FIGURE 6.1 shows the daily cash flows for a forward and a futures contract having identical terms. The futures contract generates intermediate cash flows the forward doesn t. As with the forward contract, the delivery price specified in the futures contract is set so that at initiation, the pres-... 

As illustrated in figure 6.1, the process works as follows After day one, the future price is reset from A to F. The amount (Fi - F), if positive, is handed over by the short counterparty to the long counterparty. If the amount is negative, it is paid by the long counterparty to the short. On the expiry day, T, of the contract, the long counterparty receives a settlement amount equal to Pt - F -i, which is the difference between the future price and the price of the underlying asset. The daily cash flows cancel each other out, so that at expiry the value of the contract is identical to that for a forward, that is Pj — F). 

The futures strategy is more involved, because of the margin cash flows that are received or paid daily during the term of the trade. On day one, r contracts are bought, each priced at F. After the close that day, Fi — F is received. The position is closed out, and the cash received is invested at the daily rate, r, up to the expiry date. The return on this investment is Thus, on expiry the counterparty will receive rfi -... 

The next day, futures contracts are bought at a price of F. At the close, the cash flow of F2 — F[ is received and invested at generating a return on expiry of r ( 2 This process is repeated until the... 

Aside from how they are constructed and traded, the most significant difference between forwards and futures, and the feature that influences differences between their prices, concerns their cash flows. The profits or losses from futures trading are realized at the end of each day. Because of this daily settlement, at expiration all that needs to be dealt with is the change in the contract value from the previous day. With forwards, in contrast, the entire payout occurs at contract expiry. (In practice, the situation is somewhat more complex, because the counterparties have usually traded a large number of contracts with each other, across a number of maturity periods and, perhaps, instruments, and as these contracts expire, they exchange only the net loss or gain on the contract.)... 

International trade in lead scrap is generally more volatile than trade in concentrates. This is because the quantities of scrap traded are usually smaller, and are often sold as spot tonnages, rather than under long-term contract. International flows of scrap are largely determined by specific (perhaps temporary) local shortfalls or surpluses in supply, requiring the movement of material between countries. They will also be influenced by metal price differentials, with scrap attracted to regions where local premiums allow secondary producers to offer favourable terms. 

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