On this page
Identify the unobserved date
Suppose only one-year and two-year factors are supplied, but a payment arrives at 1.5 years. A pricing schedule requires D(0,1.5). The two endpoint values do not by themselves state that factor.
Name the interpolated quantity
A straight line in zero rates is different from a straight line in discount factors or their logarithms. Each is an explicit modeling choice. Identical endpoint prices can therefore support different intermediate prices.
| Target | What the straight line connects |
|---|---|
| Discount factors | D values |
| Log discount factors | Natural logarithms of D |
| Annual zero rates | Effective spot percentages |
Retain the selected convention
The worked midpoint example compares two simple rules without declaring a universally best market curve. Label the method and interval so a reviewer can reproduce the chosen value. More elaborate curve construction may enforce additional smoothness or instrument-fitting conditions.
Treat a missing endpoint as another problem
Interpolation stays between available nodes. Extending beyond the final maturity is extrapolation and needs another assumption. A spreadsheet that silently extends the last displayed rate should not be described as using only observed data.