Interpolation

When data are available only at certain points, interpolation fills in the gaps. The simplest form, linear interpolation, assumes the value changes in a straight line between known points.

For example, if the two-year interest rate is 4% and the five-year rate is 5%, a linear interpolation estimates the three-year rate as about 4.33%, a third of the way between them, since three years is one third of the distance from two to five.

Interpolation is widely used in finance. Analysts interpolate yield curves to find rates for maturities that are not directly quoted, estimate values between data points in tables and fill in missing data in time series.

More sophisticated methods, such as cubic splines, fit smooth curves through the known points, which can be more realistic for yield curves. Interpolation is generally more reliable than extrapolation, because it stays within the range of known data, but it still assumes the pattern between points is smooth and predictable.