# Government Bond Curves

BlueGamma constructs government bond yield curves using a market snapshot approach, capturing real secondary-market pricing at specific points in time.

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## 1. Data Inputs

### US Treasuries

* **Source:** Constant Maturity (CMT) yields from actively traded Treasury securities
* **Frequency:** Updated every minute during trading hours
* **Short end:** SOFR deposit rates for maturities under 1 year

### Other Countries

* **Source:** Verified daily government bond yield data from institutional providers
* **Coverage:** UK Gilts, German Bunds, French OATs, and other sovereign curves
* **Frequency:** Daily updates reflecting end-of-day levels

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## 2. Curve Construction

### Methodology

1. **Validation** — Raw yields are checked for outliers and staleness
2. **Bootstrapping** — Zero-coupon yields derived from bond prices
3. **Interpolation** — Log-cubic method for smooth curve shapes
4. **Extrapolation** — Constrained beyond longest maturity

### Interpolation

We use piecewise log-cubic interpolation on discount factors, which:

* Ensures no-arbitrage conditions
* Produces stable forward rates
* Allows yield extraction at any maturity within the curve range

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## 3. US Treasury Conventions

| Convention  | Value              |
| ----------- | ------------------ |
| Day Count   | Actual/Actual ISMA |
| Compounding | Semi-annual        |
| Calendar    | US Government Bond |
| Settlement  | T+1                |
| Output      | Zero-coupon yields |

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## 4. Supported Countries

| Country        | Bond Name        | Currency |
| -------------- | ---------------- | -------- |
| 🇺🇸 US        | Treasuries       | USD      |
| 🇬🇧 UK        | Gilts            | GBP      |
| 🇩🇪 Germany   | Bunds            | EUR      |
| 🇫🇷 France    | OATs             | EUR      |
| 🇮🇹 Italy     | BTPs             | EUR      |
| 🇪🇸 Spain     | Bonos            | EUR      |
| 🇯🇵 Japan     | JGBs             | JPY      |
| 🇨🇦 Canada    | Government Bonds | CAD      |
| 🇦🇺 Australia | AGBs             | AUD      |

***

## 5. Data Quality

### Automated Validation

* **Shape checks** — Ensures economically sensible forward rates
* **Smoothness tests** — Detects abrupt jumps between maturities
* **Outlier detection** — Daily Z-score analysis flags unusual yields
* **Cross-validation** — Comparison against alternative data sources

### Human Review

* Daily visual inspection of all government bond curves
* Investigation of flagged anomalies before publication
* User feedback incorporated into quality review

***

## Related Documentation

* [Interest Rate Curves](/documentation/methodology/how-to-bootstrap-the-yield-curve.md) — OIS and IBOR curve construction
* [Discount Factors](/documentation/methodology/discount-factors.md) — How to calculate discount factors from yields
* [How to Pull Bond Yields in Excel](/documentation/integrations/excel-add-in/how-to-guides/how-to-pull-bond-yields-in-excel.md) — Excel Add-in guide
* [How to Calculate Discount Factors Using Government Bond Yields](/documentation/integrations/excel-add-in/how-to-guides/how-to-calculate-discount-factors-in-excel.md) — DCF calculations with Treasury yields
* [API Reference](/documentation/integrations/api/api-reference.md) — Complete API documentation


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