Chapter 2: Forwards and Futures: Mechanics and Pricing#

Imagine you run a bakery and you’re worried the price of wheat will jump before harvest. A farmer is just as worried prices might crash. You could shake hands today on a price for delivery three months from now — that’s a forward contract in its simplest form. In this chapter we build on that idea, exploring how exchanges standardised these promises into futures, how markets set their prices with cold logic, and why none of this works without margin accounts and clearinghouses standing in the middle.

The Big Picture#

We look at the two oldest and most intuitive types of derivative: forwards and futures. A forward is a custom deal between two parties; a futures contract is almost the same promise but traded on an exchange, with standardised terms and a daily money‑shuffling system that makes default almost impossible. The core question we answer is: “What should a futures price be today, given what we know about the spot price, interest rates, and costs of holding the asset?” The answer comes from a simple idea: if two ways of owning the same asset at the same future date cost different amounts, someone can lock in a risk‑free profit. Markets quickly erase such gaps, so the two costs must match. That no‑arbitrage logic is the foundation of derivative pricing, and it starts right here.

What Are Forwards and Futures?#

A forward contract is an agreement to buy or sell an asset at a specified future date (the delivery date) for a price fixed today (the delivery price). Every term — quantity, quality, place of delivery — is negotiated privately between the two parties. Because it is a custom deal, usually arranged over the counter (OTC), there is no central marketplace. The contract stays between you and the person on the other side. That means you are both exposed to the risk that the other party might not honour the deal. You carry counterparty risk: if wheat prices explode, your farmer friend might regret the handshake and vanish.

Counterparty risk: The chance that the person on the other side of a trade does not keep their promise.

A futures contract is a forward contract that has been standardised and moved onto an exchange. The exchange specifies exactly what is being traded — for example, one contract on the Chicago Mercantile Exchange (CME) might be for 5,000 bushels of No. 2 Soft Red Winter Wheat, deliverable in March, May, July, September, or December. Quality, quantity, and delivery months are fixed. The only remaining variable is the price, which gets discovered by traders in a central limit order book. Because the contract is standardised, you can buy it today and sell it tomorrow to someone else without ever taking delivery of wheat. That ease of trading makes futures markets liquid and useful.

Forward contract: A private, customised agreement to buy or sell an asset at a future date for a price agreed upon today, traded OTC with counterparty risk.

Futures contract: A standardised forward‑like agreement traded on a regulated exchange, with daily settlement and a clearinghouse acting as the buyer to every seller and the seller to every buyer.

The exchange itself does not take a view on prices. It provides the infrastructure: a rulebook, a trading platform, and — crucially — a clearinghouse that steps between the two original traders. The moment a deal is struck, the clearinghouse becomes the legal counterparty to both sides. You no longer need to trust the person you traded with; you only need to trust the financial strength of the clearinghouse, which is backed by the margin system described next.

Trading Mechanics: Orders, Margins, and the Clearinghouse#

Futures trade in the same way as stocks, with a few extra housekeeping rules. You submit an order to your broker, who routes it to the exchange. Traders use the same order types:

• Market order – buy or sell immediately at the best available price.
• Limit order – buy at a price no higher than a stated limit, or sell at a price no lower than a stated limit. An unfilled limit order sits in the order book until it matches with another trader.
• Stop order – becomes a market order once the price touches a specified trigger (the stop price). A sell stop is often placed below the market to limit losses; a buy stop is placed above the market to enter a trend.
• Stop‑limit order – once the stop price is hit, the order becomes a limit order rather than a market order. This gives you a price floor or ceiling but with the risk the order never fills.

Limit order: An order to trade only at a price at least as good as the limit price; it guarantees price but not execution.

Stop order: An order that becomes a market order when the market touches the stop price; it is often used to automatically cut losses or enter a trend.

Once you have a futures position, the mechanics that truly distinguish it from a forward kick in. You do not pay the full value upfront. Instead, you post a small deposit called initial margin — typically a few percent of the contract’s notional value (the total value of the asset the contract covers). Think of it like an earnest‑money deposit when you buy a house: it shows you are serious and provides a buffer for the exchange if prices move against you.

At the end of every business day, the clearinghouse marks your position to the settlement price. If the price moved in your favour, cash is credited to your margin account. If it moved against you, cash is deducted. This daily cash‑flow is called variation margin or daily settlement. Your account balance must never fall below the maintenance margin, which is set lower than the initial margin. If it does, you get a margin call and must top up the account back to the initial margin level. Otherwise the position may be closed out by your broker.

Initial margin: The deposit required to open a futures position, acting as a performance bond.

Maintenance margin: The minimum account equity that must be kept while a position is open; if breached, a margin call is issued.

Variation margin (daily settlement): The daily flow of gains and losses between futures accounts, ensuring credit exposures never build up.

This daily settling of gains and losses cuts counterparty risk. If a trader defaults on a losing position, the loss so far is limited to a single day’s price move, because all previous losses have already been paid. Alongside this, the clearinghouse maintains a guarantee fund and layers of loss‑sharing between clearing members. The result is a market with near‑zero default risk, even during violent price swings.

📝 Section Recap: Standardised contracts, central limit order books, diverse order types, and — most importantly — daily margin settlement via a clearinghouse give futures markets liquidity and virtually eliminate counterparty risk, something OTC forwards simply cannot offer.

No‑Arbitrage Pricing of Forwards and Futures#

Now we tackle the central question: “At what price should a forward or futures contract trade today?” The answer comes from a simple thought experiment anyone can do. Suppose we want to lock in the price of gold one year from now. There are two completely equivalent ways to own gold on that future date.

Strategy A: Buy the gold today in the spot market and store it for a year. The cost is today’s spot price, , plus any obvious carrying costs (storage, insurance) minus any income the gold might pay (gold pays none, but a stock would pay dividends). Ignoring storage costs for a moment, if we borrow the money to buy the gold at the risk‑free interest rate (continuously compounded), the total outlay grows to by time .

Strategy B: Enter a forward contract today to buy gold at the forward price for delivery in one year. We pay nothing today, but we will pay at time .

Both strategies deliver identical gold at time . Therefore, a rational market will price away any difference in cost. If , a trader could borrow money, buy gold now, sell a forward contract, and at delivery pocket a risk‑free profit of . This would push prices together until they match. The equilibrium is

This is the simplest cost‑of‑carry relationship. It says the forward price is simply the spot price plus the cost of financing the position over the contract’s life.

Real assets often need adjustments. If the asset pays a known income during the life of the contract — dividends on a stock index, for instance — that income reduces the cost of buying and holding the asset. Let be the present value of all income payments between now and . An investor who buys the spot asset receives that income, so the net upfront cost is effectively . The no‑arbitrage forward price becomes

For a continuous dividend yield , such as on a broad equity index, the spot price grows more slowly because the dividends are reinvested. The forward price formula then reads

If the asset costs money to store — crude oil tankers, wheat silos, security for gold — we treat those storage costs as negative income. Let be the present value of all storage costs. Then

or for a continuous storage rate ,

📝 Section Recap: No‑arbitrage forces the forward (and, under mild conditions, the futures) price to equal the cost of buying the asset spot and carrying it to delivery, adjusted for any income or storage costs. The basic formula is , with straightforward adjustments for dividends and storage.

Convenience Yield, Backwardation, and Contango#

The cost‑of‑carry model works well for financial assets and reliably storable commodities. But sometimes futures prices look lower than the formula would suggest. Why? Because holding a physical barrel of oil or a pile of copper gives the owner something extra: the ability to keep a factory running when supply tightens, or to profit from a sudden local shortage. This extra benefit is called the convenience yield, and it acts like a dividend that only the holder of the physical asset enjoys.

Let represent the annualised convenience yield. The futures price then becomes

When convenience yield is high enough — perhaps during a supply scare — the futures price can actually fall below the spot price. A market where is said to be in backwardation. Conversely, when , we call it contango.

Contango: A futures curve where contracts with later delivery dates trade at higher prices than near‑dated contracts, typically reflecting storage and financing costs.

Backwardation: A futures curve where later‑dated contracts trade at lower prices than the spot price or near‑dated contracts, usually driven by strong convenience yield or tight supply today.

How do backwardation and contango relate to where spot prices might go next? They don’t necessarily forecast the future. The futures price equals the expected future spot price only if investors don’t care about risk and the commodity’s price is completely unrelated to the stock market — a rare situation. In reality, the futures price includes a risk premium (an extra return for bearing risk). If producers want to hedge (sell futures), they may push the futures price below the expected future spot price, a state called normal backwardation (a term from Keynes). If consumers are the dominant hedgers (buying futures), they may bid the futures price above the expected spot, resulting in normal contango. So the shape of the curve tells you about hedging pressure and storage, not necessarily about where prices are headed.

📝 Section Recap: The convenience yield captures the non‑monetary benefit of holding physical inventory, altering the cost‑of‑carry. Depending on whether futures trade above or below spot, markets exhibit contango or backwardation, shapes driven by carry costs, supply tightness, and hedging flows.

Convergence and Payoffs#

One thing is certain: as the delivery date approaches, the futures price must move toward the spot price. At the final moment of trading — expiration — they are identical. If they weren’t, say with delivery immediately possible, you could buy the asset spot for the lower price, sell the futures to deliver it, and pocket the difference. Arbitrageurs would jump in and push the two prices together instantly. This convergence is what makes hedging and speculation with futures reliable; the contract’s value at expiry is exactly the spot price.

Convergence: The mechanical tendency for the futures price and the spot price to meet at the delivery date, enforced by arbitrage.

With that in mind, the payoff to a long futures position entered at price and held until expiration is simply . If the spot price ends higher than you locked in, you gain a dollar for every dollar above the initial futures price. If it ends lower, you lose the same amount. Graphically, this is a straight line crossing the horizontal axis at , sloping upward at 45 degrees. The short futures position has the mirror payoff: , a straight line sloping down.

Since futures are marked to market daily, the money flows in little by little each day, but the total profit or loss over the contract’s life is the same as the final payoff, plus any interest on the margin account. For most purposes, we focus on the payoff at expiry — it perfectly captures the economic effect.

📝 Section Recap: Futures prices converge to spot at expiry, eliminating any gap through arbitrage. The linear payoff profiles of long () and short () positions make futures straightforward tools for speculation and hedging.

Summary#

We began with a handshake between a baker and a farmer and ended with global exchanges processing millions of contracts a day. The deep logic is the same: a forward or futures price is not a forecast but a cost‑of‑carry number, dictated by what it takes to own the asset today and hold it until tomorrow. Standardisation, margin, and clearinghouses turn that simple agreement into a liquid, almost risk‑free tool that touches every corner of finance.