When constructing curves, are there any generic and quantitative metrics that can be computed for any kind curve (government, corporate, swap, etc)?
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$\begingroup$ Are you interested in calculating the curve's length, for any kind of curve? $\endgroup$– zetyquicklyCommented Nov 4, 2016 at 20:15
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$\begingroup$ @zetyquickly Sure, I can see that as being useful. $\endgroup$– pyCthonCommented Nov 5, 2016 at 1:55
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1 Answer
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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.
The user of the curve: The trader for whom you're building the curve may very well have strong personal preferences ("taste"). Some traders may prefer their curves to be smoother, and others like wavy ones that amplify mis-pricings in input instruments.
