A financial derivative doesn't have to give its holder a choice. The call and the put you already know are built on optionality — the right, not the obligation, to trade. Strip the optionality away and you're left with the oldest and simplest derivative of all: a plain promise to trade at a fixed price, on a fixed future date, no matter what happens to the market in between.

A wheat farmer in March doesn't know what wheat will fetch in August. An airline doesn't know what jet fuel will cost next winter. An importer who owes €1,000,000 in ninety days doesn't know what dollars it will take to buy those euros. Each of them can eliminate that uncertainty today by agreeing, right now, on the price they'll pay or receive later. That agreement is a forward contract — or, in its exchange-traded cousin's clothing, a futures contract.

The contract, in words and in symbols

A forward contract is a bilateral agreement between two parties to buy and sell an asset at a specified future time T, called maturity (or delivery), for a price K agreed today and fixed for the life of the contract. That fixed price is called the delivery price, or the forward price when we're talking about the price a brand-new contract would be written at right now. Today's market price of the underlying asset — what you'd pay to buy it on the spot, for immediate delivery — is the spot price, S_0.

The two sides have names. The party who agrees to buy the asset at K is long the forward. The party who agrees to sell it is short. Unlike an option, there is no walking away: at maturity, the long must buy and the short must sell, at K, whatever the spot price S_T turns out to be. Working out exactly how much each side gains or loses from that obligation — the contract's payoff — is the whole subject of the next lesson; here we only need the vocabulary.

A futures contract is the same idea, in different market plumbing: an agreement to buy or sell at a fixed price at a fixed future date, but standardized and traded on an organized exchange rather than negotiated privately. The next two lessons unpack exactly what that plumbing changes; for now, think of a futures contract as "a forward contract, but exchange-traded."

The last two rows are the meat of Lessons 3 and 4: how a clearing house changes who you're really trading with, and what "marked to market" means for the cash in your account. For now, notice the one thing forwards and futures share that makes them fundamentally different from a call or a put: an obligation, not a right.

Worked example: hedging jet fuel

A regional airline knows it will need 2{,}000{,}000 gallons of jet fuel in six months. Today's spot price is S_0 = \$2.60 per gallon. Worried that fuel prices might spike, the airline's treasury desk calls a bank and agrees to a six-month forward contract at a delivery price of K = \$2.68 per gallon. (Why K is a few cents above today's spot price, and not simply equal to it, is exactly the question Lesson 5's cost-of-carry argument answers — file it away for now.) The airline is long the forward: it has agreed to buy fuel at K.

Six months pass. Two scenarios:

• Fuel spikes to S_T = \$3.10. The airline still pays only K = \$2.68 per gallon under the forward — a total of \$2.68 \times 2{,}000{,}000 = \$5{,}360{,}000, instead of \$3.10 \times 2{,}000{,}000 = \$6{,}200{,}000 at the prevailing spot price. The forward saved the airline \$840{,}000.
• Fuel instead falls to S_T = \$2.20. The airline is still obligated to pay K = \$2.68 — \$0.48 per gallon more than it would have paid on the open market, a loss of \$960{,}000 relative to spot. An option would have let the airline walk away and simply buy at the cheaper spot price; a forward doesn't offer that escape hatch. That asymmetry — bounded loss for an option holder, unbounded loss (in principle) either way for a forward — is the price of not having paid an option premium up front.

Notice the airline never speculates on fuel prices here — it locks in \$2.68 and gets exactly that, regardless of which scenario plays out. That certainty, not a bet on direction, is the point of hedging with a forward.

What's actually fixed, and what isn't

The one idea worth staring at until it's obvious: K is nailed down the moment the contract is signed and never moves again. The spot price S(t), by contrast, wanders for the whole life of the contract — up, down, nobody knows in advance. The chart below sketches one illustrative path the spot price might wander along between today (t=0) and maturity (t=6 months), against the flat, fixed line at K. Drag K and watch the delivery line slide — the wandering spot path never notices; it's set by the market, not by the contract.