FRM Part 1 – Financial Markets and Products · FRM
An Introduction to Derivatives: Obligation, Right and the Line Between
A derivative is a contract whose value depends on the value of something else. That definition sounds almost empty until you notice what it permits: the contract can be traded, priced and hedged without anyone ever holding the thing it refers to.
Everything in an introductory derivatives reading follows from one distinction. Some contracts oblige both parties to transact, which makes their payoff a straight line. Others give one party a right and the other an obligation, which makes the payoff bend. Linear and non-linear is not a classification to memorise; it is the reason forwards cost nothing to enter and options do not.
Key Takeaways
- A derivative takes its value from an underlying variable, and neither party needs to own that underlying.
- Exchange traded contracts are standardised and cleared. Over the counter contracts are negotiated and carry counterparty risk.
- Forwards oblige both parties, so the payoff is a straight line and nothing is paid at inception.
- Futures share that payoff but add a clearing house and daily settlement, so the cash flow path is completely different.
- Options give one party a right, so the payoff bends at the strike and the premium is the price of that bend.
- The BIS reported $846 trillion of notional at end-June 2025 against $21.8 trillion of gross market value, about 2.6%.
What a derivative is, and the word that does the work
Derivatives are contracts whose values depend on, or derive from, the values of one or more financial variables. The underlying can be a share price, an index level, an interest rate, an exchange rate, a commodity price, a credit event, or something less obvious such as a temperature or a default rate.
Two properties follow from that dependence and are worth stating explicitly, because both surprise candidates meeting the material for the first time.
The contract does not require anyone to own the underlying. Two parties can agree today to exchange the value of a barrel of oil in six months without either of them ever intending to hold oil. That is what makes derivatives markets larger than the markets they reference.
And the contract has a value of its own that changes as the underlying moves. A forward agreed last month is worth something today, positive to one party and negative by the same amount to the other. Derivatives are zero sum between the counterparties, which is the property that makes them useful for transferring risk and dangerous when the transfer is not understood.
Where they trade: exchange and over the counter
The market divides into two venues with different trade-offs, and almost every practical difference between contract types traces back to which one they trade on.
| Exchange traded | Over the counter | |
|---|---|---|
| Contract terms | Standardised: fixed sizes, dates and specifications | Negotiated between the two parties |
| Counterparty | The clearing house, for both sides | The other party, directly |
| Credit risk | Largely removed by the clearing house and margin | Borne by each party on the other |
| Liquidity | Generally high, positions easy to close | Variable, and closing may require a new offsetting contract |
| Typical instruments | Futures, listed options | Forwards, swaps, bespoke options |
The trade-off is precision against convenience. An airline that needs to hedge exactly 1.37 million litres of jet fuel delivered in Mumbai on a specific date cannot get that from a standardised contract, and will accept counterparty risk to get exactly what it needs. A speculator with no particular date in mind prefers the exchange, where getting out is as easy as getting in.
Forwards, and the payoff that is a straight line
A forward contract commits one party to buy, and the other to sell, a specified asset at a specified price on a specified future date. The agreed price is the delivery price K, and it is set at inception so that neither party has to pay the other anything to enter. That is why a forward costs nothing at the outset: it is fair to both sides on the day it is struck.
Long forward payoff = ST − K Short forward payoff = K − ST
ST is the spot price at maturity and K is the delivery price agreed at inception
Both parties are obliged to transact, so the payoff runs in a straight line through the whole range of outcomes. The long gains one for one as the price rises above K and loses one for one as it falls below. There is no point at which either side can walk away, which is exactly why nobody pays for the privilege of entering.
A jeweller agrees today to buy 5 kg of gold in six months at a delivery price of $2,400 per ounce, taking the long side of a forward. There are 32.15 troy ounces per kilogram, so the contract covers about 160.75 ounces. What happens in three scenarios?
- Gold at $2,700 in six months: payoff per ounce = 2,700 − 2,400 = $300, so the position gains 160.75 × 300 = $48,225.
- Gold at $2,400: payoff = 0. The forward expires with no value to either side.
- Gold at $2,100: payoff per ounce = 2,100 − 2,400 = −$300, a loss of $48,225.
- In every case the jeweller pays a net effective price of $2,400 per ounce, since the loss or gain on the forward exactly offsets the movement in the spot price they pay in the market.
Answer: the hedge worked in all three scenarios, including the one where gold fell. That is the point that unsettles people new to hedging. A forward does not protect against an adverse move while leaving the favourable move intact. It removes both, and the third scenario is not a hedge failing but a hedge working.
Futures, and what the exchange changes
A futures contract is economically a forward that trades on an exchange. The obligations are the same and the payoff is the same straight line. What changes is the machinery around it, and the machinery matters.
Terms are standardised, so a contract covers a fixed quantity with fixed delivery months. The clearing house steps in between the two parties and becomes the counterparty to each, which means neither is exposed to the other’s credit. Both post initial margin, and the position is settled daily against the closing price in a process called marking to market, so a gain or loss is realised in cash every day rather than accumulating until maturity.
Daily settlement is the substantive difference, not standardisation. A forward can produce a large loss that never demands cash until the contract matures. A future demands the cash every day, which is why a position that is ultimately profitable can still fail on the way to maturity if the holder cannot fund the variation margin. The two contracts have the same payoff at expiry and very different cash flow paths, and the path is what causes real difficulties.
Options, and the payoff that bends
An option gives its holder a right rather than an obligation. A call gives the right to buy the underlying at the strike price; a put gives the right to sell at it. The seller, or writer, carries the matching obligation and has no choice in the matter.
Long call payoff = max(ST − K, 0) Long put payoff = max(K − ST, 0)
the writer’s payoff is the negative of each, and both are before the premium
The maximum function is the whole difference. It says the holder never has to take the loss, because they can simply decline to exercise. That asymmetry has to be paid for, and the price of it is the premium.
Above the strike the two contracts are indistinguishable: both pay the spot price minus K, one for one. Below the strike the forward keeps losing and the option stops at zero. The shaded triangle in the figure is the entire economic difference between the two instruments, and the premium is what the market charges for it.
A call with a strike of $60 trades at a premium of $8. Compare the outcome with a forward struck at $60, at three prices on the expiry date.
- Spot at $85. Call payoff = max(85 − 60, 0) = $25, so profit after premium = 25 − 8 = $17. Forward payoff = 85 − 60 = $25, with no premium, so profit = $25.
- Spot at $60. Call payoff = 0, so the loss is the $8 premium. Forward payoff = 0, so profit = $0.
- Spot at $35. Call payoff = 0, loss = $8 premium. Forward payoff = 35 − 60 = −$25, so loss = $25.
- The breakeven for the call is the strike plus the premium, 60 + 8 = $68. Below that the forward is better; above it the forward is better by exactly $8.
Answer: the call is worse in every scenario where the price rises and better in every scenario where it falls far enough. The $8 caps the loss at $8 and costs $8 of every gain. Nothing has been avoided for free, which is the correct way to read every option premium.
| Forward | Future | Option | |
|---|---|---|---|
| Obligation | Both parties | Both parties | Writer only. The holder has a right |
| Payoff shape | Linear | Linear | Non-linear, kinked at the strike |
| Paid at inception | Nothing | Initial margin, which is a deposit and not a cost | The premium, which is a cost |
| Settlement | Once, at maturity | Daily, in cash | At exercise or expiry |
| Maximum loss, long side | The full delivery price if the underlying goes to zero | The same, but realised along the way | The premium |
| Venue | Over the counter | Exchange | Either |
One row in that table is the most common source of confusion. Initial margin on a futures position is a performance deposit that is returned when the position is closed, so it is not comparable with an option premium, which is spent. A candidate who treats margin as the cost of a futures position will misprice the comparison every time.
Who is on the other side
Every derivative has two sides, and the participants are conventionally grouped by what they are trying to achieve.
Hedgers hold an existing exposure and use a derivative to reduce it. The jeweller above is hedging: they will buy gold regardless, and the forward fixes the price. A hedger is not trying to make money on the derivative and would happily see it expire worthless.
Speculators take on exposure they did not previously have, because they hold a view. Derivatives are attractive to them for the leverage: a futures position controls a large notional for a small margin deposit, and an option premium is a fraction of the underlying’s price. The same leverage magnifies losses at exactly the same rate.
A useful check on the categories: the same trade can belong to any of the three, and only the trader’s other holdings decide which. An oil producer selling crude futures is hedging. A fund with no oil selling the same contract is speculating. A trader selling it while simultaneously buying the physical barrel and financing the storage is arbitraging. The contract is identical in all three cases. What differs is what sits beside it, which is exactly why an institution has to look at the whole book rather than the trade.
Arbitrageurs seek riskless profit from inconsistent prices across markets, buying in one and selling in the other. Their trades are usually small in profit and large in size, and their collective effect is to keep related prices in line, which is what makes the pricing relationships in the curriculum hold at all.
The classic failures are not failures of the instruments. Nick Leeson lost around £827 million at Barings Bank in 1995 on unauthorised positions in Nikkei futures and options, enough to destroy a bank that had traded since 1762. Jerome Kerviel’s unauthorised positions cost Societe Generale about €4.9 billion in 2008. In both cases someone employed to hedge or to make markets was in fact speculating, and the leverage that makes derivatives efficient for hedging made the losses accumulate faster than the controls could see them. The lesson is about the gap between the mandate and the position, not about the contracts.
How big the market is, and why the headline number misleads
The Bank for International Settlements reported notional amounts outstanding in over the counter derivatives of $846 trillion at end-June 2025, a rise of 16% on the year and the largest annual increase since 2008. Interest rate derivatives make up 79% of that total. Foreign exchange contracts account for $155 trillion, of which around $100 trillion matures within a year. Credit derivatives grew fastest of the smaller categories, at 23%.
That headline figure is quoted often and understood rarely. Notional is the reference amount used to calculate payments, not an amount anyone owes. A $10 million interest rate swap does not put $10 million at risk; it puts the difference between two interest streams at risk.
The BIS reports a second figure for exactly this reason. Gross market value, the cost of replacing all outstanding contracts at market prices, was $21.8 trillion at the same date. That is about 2.6% of the notional total, and it is the closer measure of what is actually at stake, before any netting or collateral is taken into account.
Keep four things straight and most introductory questions become mechanical. Forwards and futures oblige both parties, so their payoffs are linear and no premium is paid. Options give one party a right, so the payoff bends at the strike and a premium is paid. Futures differ from forwards through the clearing house and daily settlement, not through the payoff. And notional is a reference amount, never an exposure.
The short version
- A derivative takes its value from an underlying variable, and neither party needs to own that underlying.
- Exchange traded contracts are standardised and cleared. Over the counter contracts are negotiated and carry counterparty risk.
- Forwards oblige both parties, so the payoff is a straight line and nothing is paid at inception.
- Futures share that payoff but add a clearing house and daily settlement, so the cash flow path is completely different.
- Options give a right, so the payoff bends at the strike and the premium is the price of that bend.
- The BIS reported $846 trillion of notional at end-June 2025 against $21.8 trillion of gross market value, about 2.6%.
Frequently Asked Questions
What is a derivative?
A contract whose value depends on, or derives from, the value of one or more underlying variables: a share price, an index, an interest rate, an exchange rate, a commodity price or a credit event. Neither party needs to own the underlying, which is why derivatives markets are far larger than the markets they reference.
What is the difference between a forward and a future?
Economically very little at expiry, since both oblige the parties to transact and both have the same linear payoff. The differences are in the machinery. A future is standardised, trades on an exchange, has the clearing house as counterparty and is settled daily in cash. A forward is negotiated, carries direct counterparty risk and settles once at maturity. The daily settlement is the substantive difference, because it demands cash along the way.
Why do options cost money when forwards do not?
Because an option gives one party a right and the other an obligation, which is not a fair exchange without payment. A forward obliges both parties equally, so its terms can be set to make it worth nothing to either side at inception. The option premium is the market price of the holder’s right to walk away, and on a payoff diagram it is the price of the region where the option pays nothing and the forward keeps losing.
What makes a payoff linear or non-linear?
Whether either party can decline to transact. Forwards and futures oblige both sides, so the payoff runs in a straight line through every outcome. Options let the holder decline, so the payoff is flat on one side of the strike and sloped on the other. Linear and non-linear is a consequence of obligation versus right, not an independent classification.
Who uses derivatives?
Hedgers, who hold an exposure and use the contract to reduce it. Speculators, who take on exposure because they hold a view and are attracted by the leverage. And arbitrageurs, who exploit inconsistent prices across markets and, in doing so, keep related prices in line.
Does a $846 trillion notional mean that much is at risk?
No. Notional is the reference amount used to calculate payments, not an amount owed. The BIS reports gross market value alongside it, which is the cost of replacing all outstanding contracts at market prices, and that stood at $21.8 trillion at end-June 2025, about 2.6% of notional. Netting and collateral reduce the exposure further still.
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