Basis Swap

An interest rate swap exchanges fixed for floating. A basis swap exchanges floating for floating — two different reference rates on the same currency and notional, say a rate that resets every month against one that resets every three months, with a small spread on one leg to balance the deal.

Why would anyone trade the difference between two floating rates? Because the differences are real money at scale. Different reset frequencies carry different bank-credit and liquidity content; a bank whose assets earn one index while its funding pays another has basis risk on its entire balance sheet — and the basis swap is the tool that hedges it. The spread is quoted in single basis points, and the notionals run to trillions.

The concept's most famous stress test: before 2008 the spread between 3-month interbank rates and overnight-indexed rates was ~5bp and treated as a curiosity. In the crisis it hit 365bp. "Floating is floating" stopped being true in one week, and an entire re-plumbing of finance — the multi-curve revolution, eventually the death of LIBOR — followed from that chart.

The contract

Both legs float; one carries the quoted spread \(b\):

Classic single-currency pairs: 1-month vs 3-month tenor basis (in the LIBOR era, "1s3s", "3s6s"), IBOR vs overnight (the LIBOR-OIS basis), and today's survivors — term-rate vs compounded overnight, and jurisdictional pairs like Euribor vs €STR, whose basis still embeds bank credit content the way LIBOR-OIS did.

The cross-currency cousin — where basis got famous

The cross-currency swap should, by covered interest parity, price flat. It doesn't: the cross-currency basis — most-watched in EUR/USD and USD/JPY — is the premium non-US banks pay for dollars through the swap market. It goes structurally negative when dollar demand outruns dollar supply:

Quarter-ends, year-ends and every dollar-funding squeeze print in this number; central-bank swap lines exist to cap it.

Who uses which basis

• Bank ALM desks: match asset and liability indices across the book — the biggest structural users.
• Issuers: a European company issuing dollar bonds swaps proceeds back via cross-currency basis — the basis level decides whether "cheap" dollar funding actually was.
• Relative-value funds: trade basis mean-reversion around quarter-ends and policy shifts, warehousing what dealers won't.

Multi-curve pricing: why basis broke the textbook

Pre-2008, one curve both projected forward rates and discounted cash flows. Non-zero basis makes that inconsistent: each index needs its own projection curve, calibrated jointly to vanilla swaps and basis swaps, while discounting follows the collateral rate (OIS for cleared trades):

with forwards \(F^{(k)}\) each read off their own curve. The machinery — curve bootstrapping as a joint fit across swap, basis and FX-forward markets — is now the first chapter of every rates quant's job, and it exists because a "curiosity spread" went to 365.

What drives the cross-currency basis

• CIP deviation as balance-sheet pricing: post-crisis leverage rules made arbitraging the basis capital-expensive; the basis is the rent on scarce dealer balance sheet (Du–Tepper–Verdelhan formalised it). It widens at reporting dates because balance sheet is scarcest exactly then — the "window dressing" sawtooth.
• Structural flow imbalance: Japanese and European institutions structurally demand dollars (hedging US assets); US institutions don't symmetrically demand yen or euros. The sign of the basis is the sign of that queue.
• Central-bank swap lines put a soft ceiling on funding stress: when the Fed's lines price through the basis, usage explodes (March 2020: $450bn) and the basis snaps back — the closest thing the offshore dollar system has to a lender of last resort, priced live.

Post-LIBOR residue

The RFR transition killed the tenor-basis complex (compounded SOFR has one flavour) but created new ones: term-SOFR vs compounded-SOFR basis (a one-way market regulators actively cap), Euribor's survival making EUR the last two-curve major, and legacy-fallback basis embedded in transitioned contracts. Basis never dies; it migrates to wherever two conventions coexist.

The formulas above are standard textbook formulations, simplified for teaching. They explain the mechanism — they are not a valuation tool, and they will not reproduce a dealer’s price.