Cross-Currency Basis Swaps Explained
Cross-currency basis is the spread required to exchange funding between currencies when observed FX forwards differ from the covered-interest-parity relationship implied by the relevant collateral curves. It is a balance-sheet and funding price, not an arbitrage-free lunch.
From covered interest parity to basis
With domestic currency \(d\), foreign currency \(f\), spot \(S_{d/f}\), and discount factors,
F_CIP(0,T) = S(0) * P_f(0,T) / P_d(0,T)
The formula assumes both curves are consistent with the collateral convention. Market forwards often imply a deviation, parameterized through a basis spread added to one floating leg. If the domestic leg pays SOFR + b, solve b such that the discounted domestic and foreign legs have equal value after FX conversion.
| Driver | Typical basis effect |
|---|---|
| USD funding scarcity | wider non-USD/USD basis |
| quarter-end balance sheet | temporary widening |
| hedged foreign bond demand | persistent directional pressure |
| credit or liquidity stress | wider, more volatile basis |
The instrument
A cross-currency basis swap exchanges notionals at spot, exchanges floating coupons in each currency, and re-exchanges notionals at maturity at the original FX rate. The initial and final notional exchanges matter: omitting them mistakenly converts the trade into a rate swap with an FX conversion.
For domestic collateral, convert each foreign cash flow using an FX forward consistent with that collateral agreement, then discount domestically:
PV_f in d = Σ CF_f(Ti) * F_d/f(0,Ti) * P_d(0,Ti)
PV = PV_domestic_leg - PV_f in d
The identity is a pricing representation. In production, construct collateral-consistent curves and validate the resulting forward curve against FX swap quotes.
def foreign_leg_pv_domestic(cashflows_f, fx_forwards, df_domestic):
return sum(cf * fx * df
for cf, fx, df in zip(cashflows_f, fx_forwards, df_domestic))
def basis_pv01(domestic_annuity, foreign_annuity_in_domestic):
# Value change for a one-basis-point spread change on either quoted leg
return 1e-4 * (domestic_annuity + foreign_annuity_in_domestic)
Risk decomposition
Basis swap P&L is not just FX delta. Key risks include domestic and foreign rates, cross-currency basis nodes, FX spot, FX forward curves, and collateral discounting. A static hedge of spot does not neutralize rolling-forward exposure; a rolling FX hedge itself realizes basis.
| Risk report | Useful question |
|---|---|
| FX delta | What is the immediate spot exposure? |
| rate DV01 by currency | Which rate curves move PV? |
| basis DV01 | What does a 1 bp basis widening do? |
| FX-forward sensitivity | Is tenor risk hedged? |
| collateral sensitivity | Does a CSA change alter valuation? |
A strategy lens
The “basis trade” often compares synthetic funding with cash funding. A positive expected carry must cover bid-offer, margin, funding, capital, credit limits, and the possibility that the basis widens precisely when liquidity is needed. Treat it as a relative-value position with liquidity beta, not a mechanically riskless CIP arbitrage.
This resembles carry trading: a carry signal can compensate for financing stress risk. Diversify by funding currency and tenor, and size from stress scenarios rather than historical daily volatility alone.
Implementation controls
Reconcile market quotes, conventions, curves, and collateral currency daily. Test that a newly struck market swap has near-zero PV, then run finite-difference checks against basis and FX-forward bumps. For historical research, avoid treating a quoted basis series as a freely investable return: it requires a specific funding and collateral implementation.
Key takeaways
- Basis is a collateral- and balance-sheet-dependent price of cross-currency funding.
- Value both coupon and notional exchanges using collateral-consistent FX forwards.
- Hedged carry still contains basis, liquidity, roll, and funding-tail risk.
Data and backtest discipline
Use executable bid and offer quotes for both FX swaps and interest-rate instruments; midpoint basis carry is not a realized return. Align spot cut, curve timestamp, and holiday calendars across currencies. An apparent basis dislocation can be caused by settlement-date mismatch or inconsistent turn adjustments rather than economic value.
Backtests should finance margin and roll notional exchanges at observable funding rates. Stress the periods when basis widened most, including quarter-end and systemic shocks, and impose exit haircuts that grow with market stress. The relevant question is whether the strategy survives its funding scenario, not whether its unlevered historical mean spread is positive.