What are smoothing splines and when should I use them over bootstrapping?

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AcadiFi · Accepted Answer

Smoothing splines fit a continuous, differentiable curve to observed bond prices by minimizing a penalized loss: the sum of squared pricing errors plus lambda times the integrated squared second derivative. A large lambda produces a stiffer, smoother curve; small lambda tracks data points more tightly. The Fisher-Nychka-Zervos spline is a common FRM-tested variant.

Consider thirteen Treasury bonds with bid-ask spreads. A bootstrap using only thirteen maturities produces thirteen kinks and potentially negative forward rates between nodes. A cubic B-spline with knots at one, three, seven, and twenty years yields a smooth forward curve while keeping pricing errors under three basis points for liquid bonds.

Use splines when you need smooth forward rates for derivative pricing, when data is noisy, or when you must interpolate across sparse maturity buckets. Use bootstrapping when you have clean, closely-spaced maturities and need exact repricing of benchmark bonds. In practice, central banks like the Fed publish Nelson-Siegel-Svensson curves, which are parametric cousins of splines producing economically meaningful level, slope, and curvature factors.

What are smoothing splines and when should I use them over bootstrapping?

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