Inputs
Covered IRPIRP Forward Curve & Bands
Bands use bid/ask and lend/borrowResults
Parity forward (mid)
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Annualized forward premium
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Parity band at tenor
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Market forward band
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Effective id (mid)
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Effective if (mid)
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Covered interest differential
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Arbitrage signal
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Scenario overlays
A/B/C lines on the chart| Enable | Name | id% | if% | Color |
|---|---|---|---|---|
Scenarios reuse spot, tenor, basis, and compounding from Inputs.
Example scenarios
Click “Load” to prefill| Domestic | Foreign | Sbid | Sask | id,l% | id,b% | if,l% | if,b% | Tenor(d) | Basis | Comp | n |
|---|
Formula used
Covered interest rate parity connects spot and forward exchange rates with domestic and foreign interest rates over horizon T years:
F_theory = S × ( 1 + i_d,eff ) / ( 1 + i_f,eff ) Effective rates by compounding: • Simple: i_eff = i × T • Periodic: (1 + i/n)^(n×T) − 1 • Continuous: e^(i×T) − 1 With bid/ask and lending/borrowing, a conservative no-arbitrage band is: F_min ≈ S_bid × (1 + i_d,eff,lend) / (1 + i_f,eff,borrow) F_max ≈ S_ask × (1 + i_d,eff,borrow) / (1 + i_f,eff,lend) Implied-rate solver from a target forward F_target: Let R = F_target / S and let f_f = (1 + i_f,eff) and f_d = (1 + i_d,eff). Then • Solve i_d: f_d = R × f_f ⇒ invert compounding to annual i_d • Solve i_f: f_f = f_d / R ⇒ invert compounding to annual i_f
How to use
- Enter currencies and spot bid/ask; choose tenor, basis, and compounding.
- Enter lending and borrowing rates for both currencies, or keep defaults.
- Pick Mode: compute forward, or solve an implied rate from F.
- Optionally add market forward bid/ask to compare against parity bands.
- Enable scenario overlays to visualize alternative curves on the same chart.
- Export results and curves as CSV or PDF.
Conventions vary by market; verify quote basis (domestic per foreign) before use.
FAQs
Bid/ask in spot and forward, and lending/borrowing differences widen a no‑arbitrage band. If quoted forwards fall outside this band, covered arbitrage opportunities may exist after costs.
It shows a conservative region of forwards compatible with covered parity given your spot and rate spreads. The mid parity line uses mid‑style rates for interpretability.
We algebraically invert the compounding formulas. For example, with periodic compounding: id = n × ( (R×ff)^(1/(nT)) − 1 ), where R = F/S.
For clarity, scenarios reuse spot, basis, compounding, and horizon. Adjust their rates and names to reflect different macro views. If you need full per‑scenario controls, extend similarly.
Dealers include collateral conventions, basis spreads, day‑count nuances, and credit/funding costs. Ensure your inputs match the quoting market and collateral currency.