Evaluating Yield Curve Fits with RMSE and Use-Specific Criteria

Summary

The document presents root mean squared error (RMSE) as a common quantitative measure of how closely a fitted curve reproduces its input market prices or yields. It is calculated from the squared differences between observed inputs and values implied by the curve, averaged and square-rooted. Curve builders often minimize this error during fitting, making RMSE a straightforward way to compare fit quality on the chosen instruments.

The answer cautions that one metric cannot define a good curve for every application. A valuation curve may be expected to reproduce benchmark instruments closely, while a relative-value curve should be judged by whether its spreads support useful, potentially mean-reverting signals. For risk management, stability of the resulting risk measures may matter more. Thus, evaluation should reflect the curve’s intended use and its users. The response offers these criteria conceptually; it supplies no empirical comparison, thresholds, or detailed procedure for assessing signal quality or risk stability.

Key ideas

• RMSE measures the typical squared-error fit between market inputs and curve-implied values.
• Curve construction commonly minimizes RMSE over the selected instruments.
• A valuation curve may prioritize accurate benchmark pricing.
• Relative-value and risk curves require evaluation criteria suited to their trading or risk purpose.

Tags

# Metrics for curve quality


# Metrics for curve quality












When constructing curves, are there any generic and quantitative metrics that can be computed for any kind curve (government, corporate, swap, etc)?

## Answer by Helin (score 2)

https://quant.stackexchange.com/a/30878

RMSE (root mean squared error) is by far the most commonly used quantitative measure for the "goodness-of-fit" of a yield curve. It is simply given by: $$ \text{RMSE} = \sqrt{\frac{\sum_{i=1}^n (P_i - \hat{P}_i)^2}{n}}, $$ where $P_i$ is the market price (or yield) of an input instrument, and $\hat{P}_i$ is its price calculated using the curve. RMSE is usually the quantity you minimize when building a fitted curve.

But IMHO, curve fitting is actually more art than science. The proper metrics for curve evaluation depends on what your curve is used for and who is using the curve, amongst other things:

- The purpose of the curve: A yield curve used for valuation should probably be able to price all benchmark instruments perfectly (i.e. RMSE should be 0). A yield curve used for relative value trading should be optimized to generate tradable signals (e.g., bond spreads to the fitted curve should be mean-reverting). A yield curve used for risk management should generate stable risk analytics.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.