Rates Derivatives

This marketWhat it is, what trades, and the ideas it runs on.

The market at a glance

Interest-rate derivatives are the largest financial market in existence measured by notional amounts outstanding — a total that runs to several times world GDP. That sounds absurd until you realise what it does: every bank hedging its loan book, every corporate fixing its borrowing costs, every pension fund matching liabilities and every mortgage system on earth routes its rate risk through these contracts. Notional measures traffic, not risk — but the traffic is the global economy's.

Since the 2008 reforms, this market runs through central clearing (LCH clears the majority of global swaps) with daily margining, and since the LIBOR transition it prices off overnight risk-free rates (SOFR, €STR, SONIA). It is the most institutionally mature derivatives market — and the one where central banks' intentions are priced second by second.

The curve is the product

Everything here trades pieces of one object: the forward curve of interest rates. An OIS reads central-bank expectations; a FRA isolates one future period; an interest rate swap bundles a strip of them; STIR futures list the same forwards on-exchange; bond futures package long-maturity risk with a delivery puzzle. On top sits the options layer — swaptions and caps/floors — pricing how uncertain those forwards are. Inflation swaps split nominal rates into real rates plus breakeven inflation.

Interactive: swap mark-to-market & DV01Medium

You pay fixed on a swap struck at K. Rates move to S — what's your position worth, and how sensitive is it?

Notional $M Contract fixed rate K % Current par rate S % Remaining years Discount rate %

Annuity factor

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DV01

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Payer MTM

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Receiver MTM

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Annual payments, flat continuous discounting — the textbook skeleton of \(V = (S-K) \times A \times N\). Real desks bootstrap full curves; the intuition is identical.

Reading central banks through this market

When headlines say "markets price a 70% chance of a cut", the source is meeting-dated OIS and STIR futures. The mechanics are simple division: if the next-meeting OIS sits 17.5bp below the current rate and a cut is 25bp, the implied probability is 70%. The OIS page walks through it — after which you'll never read a Fed-watching article the same way.

How the products fit together

All of it is built from one instrument. An interest rate swap exchanges a fixed rate for a floating one, and everything else here is that trade with one thing changed. Change the floating side to an overnight rate compounded daily and it is an overnight index swap, which is why that curve is read as what the market expects the central bank to do. Change both sides to floating and it is a basis swap, which prices nothing but the difference between two indices. Change the floating side to an inflation print and it is an inflation swap; change it to a point on the swap curve itself and it is a constant maturity swap.

Shorten a swap to one period and it is a forward rate agreement — one settlement, one forward rate, and the raw material of the curve. Exchange-trade that single period and it is a STIR future, quoted as 100 minus the rate so that it moves the same direction as a bond. Do the same to a long bond and it is a bond future, whose price is decided by whichever deliverable bond is cheapest — the one place in this market where a contract's behaviour depends on a choice the seller makes.

Two products stop being linear. Caps and floors are a strip of options on the floating rate, so a borrower pays a premium rather than giving up the upside; a swaption is one option on the whole swap. Those two are where volatility enters, which is why the same desk that quotes a swap in basis points quotes these in vol.

Concepts to master

• DV01 thinking — positions are dollar-per-basis-point numbers, aggregated across the curve in maturity buckets.
• Forwards, not spots — every curve trade is a claim that some forward rate is wrong. Decompose before you trade.
• Convexity is everywhere — futures vs. swaps, cash-settled vs. physical swaptions, long bonds vs. short: second-order terms are first-order money at institutional size.
• Vol as an asset — the swaption grid prices rate uncertainty; its level (watch 1y10y normal vol) is macro's fear gauge.

Interactive: implied forward rateMedium

Two points on the yield curve always contain a hidden third number: the rate the market implies for the period between them — the raw material of every FRA and futures quote.

Zero rate to t₁ % t₁ (years) Zero rate to t₂ % t₂ (years)

Implied forward t₁ → t₂

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Curve slope (r₂ − r₁)

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Reading

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Simple-rate approximation: f = (r₂t₂ − r₁t₁)/(t₂ − t₁). An inverted curve puts the forward below both spot rates — the market pricing cuts.

The same questions, asked of all elevenThese sections answer the same thing on every asset class, so the answers can be read next to each other.

The units this market speaks in

• Notional is the size of the contract and almost never the size of the risk. The position is DV01 — what a one basis point move is worth — and a desk states its book that way rather than in billions.
• Receiver and payer describe the fixed leg. Receiving fixed is long duration: it gains when rates fall. Getting this the wrong way round in an interview is the fastest possible way to end one.
• Short-term interest rate futures are quoted as 100 minus the rate. Buying the future is a bet that rates fall, which feels backwards until you say it out loud twice. STIR future.
• Volatility here is quoted in basis points, not in percent. Normal (basis-point) volatility rather than lognormal, because a rate can be zero or below and a percentage volatility cannot describe that. Swaption.
• The swap spread is the swap rate minus the government yield, in basis points, and it is a market in its own right rather than an error term.
• Curve trades are quoted as a difference. "Fives-thirties at plus forty" is one number describing two maturities, and it moves for reasons neither maturity moves alone. The yield curve.

Who is choosing, and who is forced

This market has a structural feature the others do not: some of its participants have to hedge more as the market moves against them, which turns a move into a bigger move.

• Forced, and self-amplifying: mortgage convexity hedgers. A portfolio of mortgages gets longer in duration as rates rise, so the hedger must sell duration into a rising-rate market — and buy it back into a falling one. The hedge chases the move.
• Forced: liability-driven pension mandates. The same mechanism as in cash bonds, executed here because swaps are the efficient instrument for it.
• Half-forced: corporates fixing floating debt at issuance. The timing is chosen; the direction is not.
• Forced by documentation: anybody posting collateral. A move against the position produces a cash call, and the cash has to come from selling something. Margin and collateral.
• Choosing: macro and relative-value funds, who are frequently on the other side of all of the above, and are paid for being there when it is uncomfortable.

What a bad day looks like here

• The shape of it: a policy surprise that moves the front end and the long end in opposite directions, so a book that was flat in duration terms turns out not to have been flat at all.
• The first tell: implied volatility rising while the rate itself has barely moved. Somebody is paying to be protected before the move.
• The second tell: the hedge chasing the market. When convexity hedgers must sell duration into a selloff, the second half of the move is caused by the first half.
• The collateral leg: being right is not a defence against a variation margin call arriving before the thesis pays. Margin and collateral.
• The question that would have caught it: what is my exposure to the shape of the curve, separately from its level?

How a trade actually happens here

This is the most industrialised settlement chain on the site. Standardisation was imposed after 2008, and one consequence is that two near-identical exposures — a swap and a strip of futures — now have very different cash flows.

• Agreeing it — a fixed rate against a floating index. The trade has no value at inception: the fixed rate is chosen so that the two streams are worth the same on day one, which is why a swap costs nothing to enter and a great deal to leave. Interest rate swap.
• Clearing is not optional for the standard shapes. The trade is novated to a central counterparty: the original pair stop facing each other and each face the clearing house, posting initial margin against a modelled worst case and variation margin against the move that actually happened.
• Variation margin is a payment, not a pledge. Cash moves each day and settles that day's change permanently. A position that has moved against you consumes cash today, whatever it will be worth at maturity — the mechanism behind the 2022 LDI episode.
• Futures do the same thing, only more visibly. The exchange marks every position to its official closing price and pays or collects the difference before the next session opens. There is no accrual and nothing left to unwind. Short-term interest rate future.
• The floating leg has dates of its own. A rate is fixed on one day and paid on another, and with an overnight index it is not knowable until the period has already passed, because it is compounded out of rates that have not happened yet. Overnight index swap.
• When it fails: a margin call is not met by its deadline. A clearing house does not negotiate — it closes the position out at the market, and the loss that gets crystallised is the market's rather than the model's.

Where the spread is, and who earns it

The largest derivatives market on earth is also the one where the quoted cost looks smallest — a fraction of a basis point — which is exactly why the cost has to be measured against the position's risk rather than its notional.

• The bid-offer is in basis points of rate, not in money. Half a basis point on a ten-year swap sounds like nothing and is a real number once it is multiplied by the DV01 of the notional traded. Quoting the cost against the notional makes it look negligible; quoting it against the risk is the honest comparison. Working it out without a screen.
• It widens with anything non-standard. An odd start date, an amortising notional, a currency the desk does not run — each is a position the dealer cannot offset against the flow it already has.
• Margin is not a fee, but it is a cost. Initial margin is returned; what it earns while posted is not what the poster would have chosen to earn on it. On a long-dated hedge that difference compounds for years. Margin and collateral.
• The valuation adjustments on an uncleared trade. A dealer facing a counterparty without daily margin prices in the credit and the funding, and hands over one number rather than three. The adjustment is inside the rate and is not itemised.
• The basis. When the instrument that hedges is not the instrument that is held, the gap between them is a cost that shows up as a surprise rather than as a charge. Basis swaps exist because that gap is itself traded.

How a position here ends

A swap is a stream of dated payments, so it has no bid to hit. Every ending below is a way of stopping those payments, and they are not equivalent.

• It runs to maturity. Payments on every reset date to the last one, which for a thirty-year trade is a relationship rather than a transaction.
• It is terminated by agreement. Both sides agree a value and one pays the other. The number is a mid plus the dealer's spread, on a position whose remaining risk may be much larger or much smaller than it was at inception.
• It is offset. An equal and opposite trade cancels the economics but not the trades: two live contracts, two sets of documentation, and margin on both — a portfolio that is flat and still expensive.
• It is compressed. A service run across many participants tears up sets of trades that are economically redundant and replaces them with fewer. This is why a market measured in notional outstanding can shrink sharply without anybody changing a view. Clearing and settlement.
• The option ends. A swaption expires worthless or turns into the swap it was written on, which is one ending that starts a longer one.
• A counterparty defaults. Close-out netting collapses every trade with that name into a single amount owed one way. The mechanism is the reason the market can be enormous without the exposures being.

Which risk decides across this class

Every product page here carries the same five bars. Read down the class instead of across one instrument, the question changes: is this a shelf of things that fail the same way, or a shelf of things that only share a department?

Which of the five decides what, across these 10

Counted from the same table each product page prints, so the two cannot disagree. Not a rating and not a ranking: it says which failure mode drives the outcome, not how dangerous anything is.

• Market10 of 10The price of the thing moves.Decides: Basis Swap, Bond Future, Cap & Floor, Constant Maturity Swap, Forward Rate Agreement, Inflation Swap, Interest Rate Swap, Overnight Index Swap, STIR Future, Swaption.
• Credit0 of 10Somebody who owes you does not pay.Decides: none of them. Matters on 4 more.
• Liquidity0 of 10You cannot get out at anything near the marked price.Decides: none of them. Matters on 2 more.
• Funding6 of 10Cash is needed before the position pays off — margin, calls, rolls.Decides: Basis Swap, Bond Future, Constant Maturity Swap, Interest Rate Swap, Overnight Index Swap, STIR Future. Matters on 1 more.
• Operational0 of 10The failure is in documents, systems, keys or people, not in prices.Decides: none of them. Matters on 4 more.

Market decides 10 of the 10 — which is what makes this a class rather than a list: the instruments differ in shape and fail the same way. Credit, Liquidity and Operational decide nothing here — which is not the same as being absent.

The same five read across all 129 instruments →

Go deeper, and practiseLonger pieces, what an interview asks here, and a page to print.

Go deeper

Interactive: FRA settlementMedium

A forward rate agreement locks a future interest rate today. At fixing, only the difference changes hands — discounted, because it's paid at the period's start.

Notional ($m) FRA rate % Actual fixing % Period (months)

Settlement (discounted)

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Who receives

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Undiscounted difference

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Settlement = N·(L−F)·τ / (1+L·τ). The buyer profits when rates fix above the agreed rate — a one-period swap, which is exactly what a swap is a strip of.

How this market works

Analysis

Market mapWho is on the other side of your trade

Prices are made by participants with different jobs, different constraints and different reasons to trade. Knowing whose need you are meeting explains more about a market than any indicator.

• Bank asset-liability desks are the structural payers and receivers, hedging deposit and mortgage books. Their flow is driven by balance-sheet shape, not by rate views.
• Pension funds and insurers receive fixed at the long end to match liabilities — the dominant flow beyond twenty years in several currencies.
• Mortgage hedgers in the US must buy duration when rates fall and sell when they rise, a convexity-driven flow that amplifies moves in the ten-year sector.
• Macro funds express views on the policy path, mostly in the front end where the priced path is most explicit.
• Clearing houses now sit between almost all of it, which changed the risk from bilateral credit to correlated margin calls.

Costly mistakesThe five mistakes that cost the most here

Not a list of ways to be clever — a list of the errors that recur, why each one is structural rather than careless, and which tool on this site settles it.

• Confusing the forward with a forecast. A forward is a hedgeable price containing a term premium; it has historically been a poor predictor and remains the correct hedging rate.
• Hedging notional instead of sensitivity. Match DV01, not face value. The swap calculator exists for exactly this.
• Forgetting the swap outlives the hedged item. When the underlying exposure disappears, the swap does not — a live and unhedged position remains.
• Assuming one interest rate. Discounting follows the collateral; forecasting follows the index. The basis between them is a real risk, not an academic detail.
• Ignoring the cash-flow profile of the hedge. Daily variation margin against an item that pays years later is the Metallgesellschaft failure in one line.

What an interview asks here

Rates questions test whether you can hold a curve in your head and say what a position is actually exposed to, in basis points of what.

Try each one out loud before you open it. What is underneath is the shape of a complete answer, not a script — somebody who can produce those parts in their own words can also answer the four variations that follow, and somebody who has memorised a paragraph can answer one.

Q1What is an interest rate swap and who uses one?

What it is checking. The workhorse instrument, and the answer must reach 'no principal moves'.

A complete answer contains:

• An exchange of a fixed rate for a floating rate on a notional amount, for a term. The notional never changes hands.
• Only the net difference is paid on each date, which is why a large notional supports a small cash flow.
• A borrower with floating debt uses it to fix; an investor with fixed assets uses it to float.
• Its value at inception is zero, and it moves as rates move — so it is a mark-to-market exposure and a margin obligation.
• Which is the point most often missed: being right at maturity does not pay a margin call today.

Read it properly: Interest rate swap · The LDI crisis, 2022

Q2What is DV01 and why is it the number a rates desk quotes?

What it is checking. Whether the candidate thinks in risk units rather than in notionals.

A complete answer contains:

• The change in value for a one basis point move in yield, expressed in currency.
• It makes positions in different instruments and maturities directly comparable, which a notional does not.
• A ten-year swap and a two-year swap with the same notional carry completely different risk; the same DV01 makes them equivalent.
• It is what a hedge ratio is built from, and what a limit is set in.
• And it is local: it needs convexity for large moves, exactly as duration does.

Read it properly: Interest rate swap · Curve construction

Q3How do you build a curve from market instruments?

What it is checking. A bootstrapping question, and the answer must be sequential.

A complete answer contains:

• Take the shortest instruments first — deposits or overnight-indexed rates — and solve for the discount factors they imply.
• Move outwards, using futures or forward rate agreements in the middle and swaps at the long end.
• Each new instrument is solved using the discount factors already determined, which is why it is called bootstrapping.
• Interpolate between the nodes, and the interpolation method is a real choice that shows up as forward-rate artefacts.
• Post-crisis, discounting and forecasting are separate curves, because collateralised cash flows are discounted at the collateral rate.

Read it properly: Curve construction · Rates derivatives

Q4What replaced the interbank offered rates and why does it matter?

What it is checking. A benchmark reform question. It is recent, structural, and frequently answered vaguely.

A complete answer contains:

• Overnight risk-free rates, compounded in arrears, replaced term rates set by panel submission.
• The reason was that the old benchmarks referenced a market that had largely stopped trading, so submissions were judgements rather than transactions.
• The practical consequence is that a period's rate is not known at the start of the period, which changes how a coupon is calculated and when.
• Hence lookbacks, observation shifts and lags in the conventions — all of which exist to give somebody time to pay.
• And a credit-sensitive borrower now pays a spread over a risk-free rate rather than a rate that already contained bank credit.

Read it properly: Curve construction · Interest rate swap

Q5What is a swaption and what is the buyer really buying?

What it is checking. An optionality question with a structural answer.

A complete answer contains:

• An option to enter a swap at a set fixed rate on a future date, as payer or receiver.
• So it is an option on the level of rates at a point on the curve, and its price is driven by rate volatility.
• A borrower planning to issue uses a payer swaption to cap the cost of the rate move before the deal.
• It is also embedded elsewhere: a callable bond is a bond plus a sold receiver swaption, which is why callable spreads behave oddly when volatility moves.
• Which means a portfolio can be short rate volatility without anybody having traded a swaption.

Read it properly: Swaption · Rates derivatives

Q6Why do pension funds use leveraged rate hedges?

What it is checking. A real-world application, and the 2022 case makes it a live question.

A complete answer contains:

• Their liabilities are decades of fixed payments, so they behave like a very long bond and are extremely rate-sensitive.
• Hedging that with physical bonds would consume the whole portfolio, leaving nothing to generate return.
• So they hedge with swaps and repo, which delivers the rate exposure for a fraction of the capital.
• The hedge is correct and the leverage introduces a liquidity obligation: variation margin is due in cash, same day.
• Being right at maturity does not pay a margin call on Wednesday, which is exactly what 2022 demonstrated.

Read it properly: The LDI crisis, 2022 · Margin and collateral

Q7What is the difference between a forward rate and an expected future rate?

What it is checking. A conceptual question that is quietly important and frequently answered wrongly.

A complete answer contains:

• A forward rate is implied by today's curve by arbitrage — it is what makes two funding paths equivalent.
• An expected future rate is somebody's forecast, and there is no arbitrage enforcing it.
• The gap between them is the term premium, and it can be positive or negative.
• So reading forwards as a forecast overstates how much the market is predicting, and understates how much is compensation for risk.
• That distinction is why carry and roll-down can be positive even when nobody expects rates to move.

Read it properly: The yield curve · Forward rates

Do these against a clock → — one at a time, ninety seconds each, answer before you look.

Whose questions these are. Every question on this page was written for this publication. None is taken from anybody else’s question bank, and none is a claim about what any named firm asks — that is neither verifiable from here nor ours to assert. They are our own reading of which mechanism a question of this kind is testing. Information and education only.

Test yourself: five questions

Five quick questions on this asset class — checked entirely on your device, nothing stored or sent. Wrong answers come with explanations; the deep dives above hold every answer. For education only.

Interactive: swaption pricer (Black's model)Hard

The right, not the obligation, to enter a swap at a fixed rate. Priced on the forward swap rate and discounted by the annuity of the underlying swap — the same annuity that gives a swap its DV01.

Notional $m Strike rate % Forward swap rate % Volatility % Option expiry (years) Swap tenor (years) Discount rate %

Annuity factor

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Payer swaption

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Receiver swaption

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Payer, in basis points

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Exercise probability

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Reading

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A payer swaption is a call on rates; a receiver is a put. Notice that the annuity — not the notional — is what scales the premium: a swaption on a 10-year swap is worth roughly twice one on a 5-year swap at the same rate, because there are twice as many payments to protect.

⬇ The whole class on one printable page

Who pays whom, drawn

The payoff charts on this site say what an instrument is worth at the end. These say who the parties are and what each one hands over — every payment between the investor and the bank on the other side, in the order it happens. Each diagram sits on its product's own page. 3 of them carry a second diagram, folded shut, for what happens after the bargain is struck — clearing, delivery, custody. That half is deliberately separate: a clearing house is not a party to the bargain.

• Interest Rate Swap — Two legs on a notional that is never lent
• Forward Rate Agreement — One payment, and it arrives at the start
• Swaption — An option whose underlying is itself a contract
• Cap & Floor — An insurance policy that pays per period
• Bond Future — You agree a price without knowing which bond you get
• STIR Future — A price quoted as one hundred minus the rate
• Inflation Swap — Fixing inflation with a single exchange at the end
• Basis Swap — Floating against floating

Who does this: Rates Derivatives is quoted from five sell-side seats — Sales, Trading, Structuring, Research, Prime Services — and held from the buy-side by Asset Management, Private Markets, Hedge Funds & Alternatives, Wealth Management, Insurance & Pensions. See the industry map.