Quick answer: FX swaps and cross-currency swaps let banks and other institutions transform funding in one currency into funding in another while hedging the exchange-rate exposure. Textbook covered interest parity (CIP) says the forward exchange rate should be pinned down by the spot rate and the two currencies’ interest rates. In real markets, the observed forward price can deviate from that frictionless relationship. The residual is called the cross-currency basis. A non-zero basis is not simply a mysterious extra interest rate: it reflects the price of balance-sheet capacity, hedging demand, funding scarcity, credit, collateral, liquidity and market frictions that prevent arbitrageurs from eliminating the gap completely.

An FX swap can remove open currency risk and still leave funding, liquidity, collateral and rollover risk.

Page role: funding conversion, not FX settlement

Bukit Timah Tutor already has How Foreign-Exchange Settlement Algorithms Reduce Principal Risk. That page owns the question “How do two currencies settle without one side paying away principal first?”

This article owns a different job: how banks mathematically transform funding across currencies and why the observed swap price can diverge from frictionless interest-parity pricing.

BIS research calls the cross-currency basis the amount by which the cost of borrowing a currency through the FX swap market differs from direct cash-market borrowing. A persistent non-zero basis therefore signals a deviation from covered interest parity. See Covered interest parity lost: understanding the cross-currency basis.

1. Start with a quote convention

Exchange-rate formulas become confusing when the quote convention is left unstated. Suppose:

S = spot exchange rate measured as units of domestic currency per one unit of foreign currency;
F = forward rate with the same quote convention;
r_d = domestic interest rate;
r_f = foreign interest rate;
T = maturity in years.

Under a simple single-period covered-interest-parity model:

F = S × (1 + r_dT) / (1 + r_fT).

With continuous compounding the same idea becomes F = S·exp[(r_d−r_f)T]. Real market pricing uses the appropriate money-market conventions, discount curves, settlement dates and collateral framework rather than this teaching approximation.

2. Why CIP should hold in a frictionless world

Imagine two ways to obtain a known domestic-currency payoff at date T:

Invest domestic currency directly at r_d.
Convert domestic currency into foreign currency at spot, invest at r_f, and lock the future conversion back into domestic currency using a forward contract.

If both routes have the same credit, liquidity and operational risk and can be scaled freely, their covered returns should match. Otherwise arbitrageurs could borrow in the cheaper route, lend in the dearer route and lock the exchange rate.

That is the textbook logic. The cross-currency basis exists because real balance sheets are not frictionless or infinitely scalable.

3. Forward points are the observable price adjustment

Market dealers often quote the difference between forward and spot as forward points rather than quoting the full forward outright.

Forward points = F − S, expressed in the market’s quote units.

If domestic interest rates exceed foreign rates under the convention above, the foreign currency tends to trade at a forward premium in domestic-currency terms. But the exact sign intuition depends on the currency pair and quote convention, so robust systems calculate from defined curves rather than memorising verbal rules.

CME describes cross-currency basis as the difference between the observed FX-forward price and the theoretical price implied by covered interest parity using spot and benchmark interest rates. See Cross-Currency Basis Watch.

4. An FX swap is two FX transactions tied together

In a standard FX swap, the parties exchange two currencies near the start and reverse the exchange at a later date using a pre-agreed forward rate. Economically, one party is borrowing one currency while lending the other for the swap period.

A simplified timeline is:

Today/spot date: give currency A, receive currency B.

Maturity: return currency B, receive currency A at the agreed forward exchange rate.

Because the exchange rate for the reversal is fixed in advance, the trade can transform funding without leaving the same open FX exposure as an unhedged foreign-currency loan.

5. A cross-currency swap extends the transformation across many coupon dates

A longer-dated cross-currency swap typically exchanges cash flows in two currencies over time and may exchange principal amounts at the start and end. Structures vary: fixed-versus-floating, floating-versus-floating and other conventions exist.

Conceptually the valuation engine must price:

cash flows in currency A;
cash flows in currency B;
discount factors appropriate to each leg and collateral arrangement;
FX conversion between present values;
the basis spread required to make the two legs have equal value at inception.

The basis is therefore part of the curve system used to make cross-currency cash flows mutually consistent with observed market prices.

6. The cross-currency basis as a residual

Suppose frictionless CIP implies a particular forward rate F_CIP, but the market forward is F_mkt. The deviation can be translated into an annualised basis spread b such that one currency’s effective funding rate must be shifted by b to reconcile the observed forward.

In schematic form:

observed forward = CIP(spot, domestic curve, foreign curve + basis).

The exact equation depends on quote, compounding, collateral and curve conventions. The important interpretation is that b is the extra price needed to balance supply and demand after real-world funding and balance-sheet frictions are included.

7. Why arbitrage does not simply erase the basis

Classic arbitrage logic assumes traders can expand positions until price differences disappear. In banking, every expansion uses scarce balance-sheet resources. It can consume leverage exposure, capital, liquidity, credit limits and collateral capacity.

BIS research links persistent CIP deviations to costly bank balance sheets and FX-hedging demand. When arbitrage requires balance-sheet capacity that has a shadow price, the “riskless” spread can persist because exploiting it is not free. See The failure of covered interest parity: FX hedging demand and costly balance sheets and The dollar, bank leverage and the deviation from covered interest parity.

This creates a deeper connection: the basis can be viewed partly as a market price of constrained intermediation capacity.

8. A worked funding comparison

Suppose a euro-area bank needs US dollars for three months. It can compare two routes:

Direct route: borrow dollars in the unsecured/secured dollar cash market.
Swap route: raise euros, swap euros into dollars today, and lock the reversal in three months.

The algorithm computes the all-in annualised cost of each route after:

cash-market funding rate;
spot/forward points;
cross-currency basis;
collateral or margin cost;
balance-sheet usage;
credit valuation and operational cost where relevant.

If swapped dollar funding is more expensive than direct dollar funding even after FX risk is covered, the difference is evidence of basis/friction rather than a free lunch available to every institution.

9. The basis curve has a term structure

One-week, one-month, three-month, one-year and five-year cross-currency basis levels need not be equal. Different maturities contain different:

funding demand;
regulatory reporting-date pressure;
hedging demand;
balance-sheet capacity;
liquidity premium;
counterparty and collateral conditions.

A pricing engine therefore bootstraps or fits a cross-currency basis curve from observed market instruments rather than treating basis as one constant spread.

This connects directly to How Yield-Curve Algorithms Build the Term Structure: the cross-currency system is a multi-curve extension in which two currency curves and FX forward/basis instruments must be mutually consistent.

10. Collateral currency changes valuation

Modern derivatives are often collateralised. The currency in which collateral is posted can affect discounting because collateral remuneration changes the effective funding economics of the derivative cash flows.

That means two trades with identical contractual coupons can have different valuation economics if their collateral agreements differ. A cross-currency pricing stack therefore needs:

contract cash-flow conventions;
collateral agreement;
discount curves consistent with collateral terms;
FX spot and forward data;
basis curves;
credit/funding adjustments where applicable.

The weak point is often not the algebra but inconsistent curve/collateral assumptions across systems.

11. FX swaps create large principal payment obligations

Unlike many interest-rate derivatives where only net value changes are exchanged, FX swaps and forwards involve contractual exchanges of full principal amounts. BIS statistics therefore emphasise that these instruments create large future currency payment obligations even though those obligations are not recorded as conventional on-balance-sheet debt.

BIS estimated that, at end-2023, dealer banks had about US$91 trillion in outstanding FX derivatives positions with the dollar on one side, of which about US$56 trillion was with customers. The important educational point is not merely the scale; it is that a derivative can create a very large liquidity obligation at maturity without looking like a conventional loan balance. See International finance through the lens of BIS statistics: the global reach of currencies.

12. Rollover risk: short swaps can fund long assets

A bank can fund a long-dated dollar asset using a sequence of short FX swaps. That can be cheap in normal markets but creates rollover risk: each swap must be renewed, and the basis can widen sharply during funding stress.

BIS work on “missing dollar debt” highlights exactly this vulnerability. Short-term FX swaps can create recurring dollar repayment needs that become difficult to refinance when global dollar funding tightens. See Dollar debt in FX swaps and forwards: huge, missing and growing.

The correct liquidity question is therefore not only “What is today’s swap rate?” but also “What happens if the swap cannot be rolled at anything close to today’s basis?”

13. Central-bank swap lines are a backstop to market funding stress

The Federal Reserve maintains standing US-dollar liquidity swap arrangements with the Bank of Canada, Bank of England, Bank of Japan, European Central Bank and Swiss National Bank. The purpose is to support foreign-currency liquidity provision and ease strains in global dollar funding markets, helping prevent those strains from impairing credit supply.

See the Federal Reserve’s Central Bank Liquidity Swaps page and the ECB explainer What are currency swap lines?.

This does not make ordinary FX-swap funding risk-free. It shows that foreign-currency funding markets can become important enough to financial stability that central-bank liquidity backstops exist for stressed conditions.

14. Settlement risk and funding risk are different

Payment-versus-payment arrangements such as CLS can reduce principal settlement risk by coordinating final exchange of currencies. But a perfectly safe settlement mechanism does not guarantee that the bank has the currency needed on settlement day.

Therefore:

settlement mechanism answers “Will both legs exchange safely?”

funding model answers “Can the bank obtain the required currency when the leg is due?”

Both can fail independently.

15. Evidence polarity: what should widen or narrow the basis?

A good model should allow evidence to move the basis in either direction. Forces associated with a wider basis can include greater one-sided hedging demand, scarce dealer balance-sheet capacity, stronger dollar funding demand, credit/liquidity stress or regulatory reporting-date pressure.

Forces that can compress the basis include stronger arbitrage capacity, lower balance-sheet cost, improved funding liquidity, reduced hedging imbalance or effective central-bank liquidity provision.

The point is not to assign one permanent sign to every driver. It is to test whether the proposed mechanism actually predicts the observed maturity, currency and time pattern.

16. Counterexamples that break naive pricing rules

“CIP deviation is free arbitrage.” Counterexample: exploiting it consumes scarce leverage, funding and collateral capacity.
“No FX risk means no risk.” Counterexample: the swap is hedged against spot FX but still has rollover and liquidity risk.
“Forward points are only interest-rate differentials.” Counterexample: observed points contain cross-currency basis and market frictions.
“The shortest funding is cheapest, therefore optimal.” Counterexample: repeated rollover creates a maturity mismatch and stress vulnerability.
“Collateral is only a credit-risk detail.” Counterexample: collateral currency changes derivative discounting and funding economics.

17. The cross-currency pricing pipeline

Fix the FX quote convention and settlement dates.
Build domestic and foreign discount/forward curves.
Compute the frictionless CIP-implied forward.
Observe market FX forwards/swaps and cross-currency instruments.
Infer forward points and basis by maturity.
Bootstrap or fit a cross-currency basis curve.
Apply collateral and discounting conventions consistently.
Value each currency leg and convert present values coherently.
Calculate all-in funding cost, not just the headline forward.
Measure liquidity, margin and rollover requirements.
Stress basis widening and failed rollover.
Reconcile pricing against independent market data and cash-market alternatives.
Monitor curve residuals and quote quality.
Update after benchmark, collateral, regulation or market-structure changes.

18. Failure modes and weak links

Quote inversion. Domestic/foreign convention is reversed inside one formula.
Single-curve pricing. One interest curve is used where collateralised multi-curve pricing is required.
Basis omission. Observed forward prices are forced to fit CIP exactly even when the market does not.
Rollover blindness. Short-term funding is treated as if permanently available.
Collateral inconsistency. Front office, risk and accounting systems discount the same trade under different collateral assumptions.
Settlement/funding confusion. PvP settlement protection is mistaken for foreign-currency liquidity.
Balance-sheet invisibility. Off-balance-sheet principal obligations are absent from liquidity stress views.
Stale basis curve. Thin market quotes are interpolated without uncertainty controls.

19. Diagnostics and falsifiers

Does the model reproduce observed forward points across maturities?
What part of all-in funding cost comes from interest differential versus basis?
How sensitive is the basis curve to collateral currency?
Which maturity contains the largest rollover concentration?
Does the pricing engine reconcile with an independent cash-and-forward replication?
How much does funding cost change if the basis widens by 25, 50 or 100 basis points?
Which principal exchanges create the largest same-day currency need?
What observation would falsify the claim that balance-sheet scarcity is driving the current basis?

Suppose someone claims, “A non-zero basis proves a risk-free arbitrage opportunity.” A falsifier is an all-in replication showing that leverage, funding, collateral, credit and operational costs consume the apparent spread, or that the institution cannot scale the trade because the binding balance-sheet constraint has a positive shadow price. Price deviation alone does not prove economically free arbitrage.

20. Verification and update triggers

reprice against independent spot and forward sources;
reconcile swap cash flows to confirmed trade conventions;
compare FX-swap implied funding with direct cash-market funding;
stress principal-exchange and margin liquidity;
validate interpolation in sparse basis maturities;
review after benchmark transitions or collateral-agreement changes;
monitor reporting-date basis dislocations separately from ordinary periods;
keep historical curves so realised funding costs can be compared with the curve available when the decision was made.

Connections across the finance-and-banking algorithms lane

Yield-curve algorithms — the domestic and foreign term structures underlying CIP.
FX settlement algorithms — how principal exchanges settle safely after pricing.
Intraday liquidity — principal legs and margin can create time-specific currency needs.
Collateral optimisation — collateral terms change the all-in economics of derivative funding.

Research anchors

The deeper lesson

Cross-currency pricing is where a textbook no-arbitrage identity meets a constrained banking system. CIP gives the clean benchmark. Forward points reveal the market price. The basis measures the gap that remains after real funding, hedging and balance-sheet constraints enter. Collateral changes discounting. Short maturities create rollover dependence. Principal exchanges create liquidity needs. A strong algorithm therefore treats the basis not as an unexplained adjustment but as evidence that the capacity to move funding across currencies is itself scarce and priced.

Educational note: This article explains public foreign-exchange and banking mathematics. It is not trading advice, hedging advice, funding advice or institution-specific treasury guidance.

Small Group Tutorials

How Cross-Currency Swap and FX-Swap Algorithms Price Funding: Covered Interest Parity, Forward Points, Basis Spreads, Collateral and Liquidity