Government Bond Curves

How BlueGamma constructs government bond yield 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

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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

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Related Documentation

• Interest Rate Curves — OIS and IBOR curve construction
• Discount Factors — How to calculate discount factors from yields
• How to Pull Bond Yields in Excel — Excel Add-in guide
• How to Calculate Discount Factors Using Government Bond Yields — DCF calculations with Treasury yields
• API Reference — Complete API documentation