Methodology

Every curve on this site is fitted rather than drawn. A cloud of individual bonds goes in, one line comes out.

There are a couple of standard answers to deriving a yield curve.

• Nelson-Siegel-Svensson. A handful of parameters, a clean functional form, published by central banks, taught in every fixed income course.
• Benchmark bonds. A single bond is chosen for each maturity on the curve — 2 years, 5, 10 — and its yield is the yield for that point. Simple and clean: no model, no parameters, nothing to argue with. It is also where most of the headline yields you read every day come from.

On deep, liquid government curves both work well enough. Yet they have some known issues.

1. As time passes, the 10yr benchmark bond becomes 9.95yr, 9.90, 9.85… and then the benchmark switches to a newly issued bond, back at 10. That instant the curve moved — not because the market moved, but because the bond underneath it was replaced.
2. Only a handful of maturities get a benchmark bond, so the curve is not really a continuous line, it's sampled at discrete points. There is no real way to get an 8.8yr value out of it, beyond simplistic interpolation.
3. And although close, 9.8yr is not 10yr. Where the curve is steep that gap is a bias in the published number, and it follows the issuance calendar rather than averaging out.

On dispersed corporate bonds, they fail miserably.

• Corporate universes are sparse and lumpy. An issuer might have eleven bonds, eight of them bunched between three and seven years, plus one lonely 2045 maturity. There is no 10-year bond to nominate as the benchmark, and no 5-year either. Svensson at least interpolates gracefully across a full maturity spectrum, but it does not cope with gaps, and that single long bond ends up dictating the shape of everything below it.
• The parameters are global, so one bad price contaminates the whole line. Corporate bonds trade thinly. Quotes go stale, sizes are small, and an off-market execution looks exactly like a real one. A least-squares fit gives it full weight, and since every parameter touches every maturity, one odd bond at four years can lift the thirty-year point. There is no locality in the model at all.
• The shape is wrong. Nelson-Siegel bakes in an assumption about what a curve looks like: level, slope, one or two humps. Credit curves don't always agree. They flatten, they kink, they invert at the front for a name the market is worried about, they step where a cluster of callable bonds sits. Forced through the model, those features either disappear or come back as a hump nobody put there.

We spent a long time patching around this: weighting schemes, constraints, aggressive pre-filtering. Every fix bought a little accuracy on one curve and broke another. Eventually it was clear that was beyond repair.

So we built our own

That took a long time. Staring at the curves that came out wrong, working out what the data was actually doing, and going back. Thousands of curves, every trading day, across every currency, rating band and sector we cover.

What we ended up with rests on three ideas.

• Outlier detection is as important as the curve fit methodology. As they say, garbage in, garbage out.
• Hierarchy is King. A narrow curve and the broader one containing it are fitted with some knowledge of each other, so a judgement made where the evidence is strongest carries into the places where it's thin.
• Continuous learning. We currently produce some 5,000-10,000 curves, with ever-changing data and curve shapes on a daily basis. Every day and every corner case is a learning opportunity to refine the methodology.

Our sources

Ratings are the median of the ratings we observe for an issuer across the public information published by rating agencies. bondScovery is not a rating agency and expresses no credit opinion of its own.

Pricing reflects publicly available end-of-day market executions and quotes. Industry classifications, issuer mappings and the other metrics on top of them are bondScovery's own independent analysis.

Found a curve that looks wrong? That's genuinely useful to us. The CONTACT form comes straight to the people who built this. Some of our better improvements started with someone pointing at a line and saying it can't be right.