Overview
Interpolation is a method of constructing new data points within the range of a discrete set of known data points. Typically, yield curve data is made available showing interest rates for several corresponding durations which must then be interpolated to find rates for durations not present in the original data. This article covers the interpolation methods available within PrecisionLender.
What Interpolation methods are available within PrecisionLender?
Interpolation method settings are located in Funding Packages. PrecisionLender offers two interpolation methods when dealing with yield curves:
- Piecewise Linear
- A simple line is drawn between each data point on the curve
- https://en.wikipedia.org/wiki/Linear_interpolation
- Monotone Convex
- If your bank is using the Caps and Floors functionality, we recommend using the Monotone Convex interpolation method. This is because the Caps and Floors functionality relies on forward rate estimates which are sensitive to artifacts within the interpolated curve (kinks).
- https://en.wikipedia.org/wiki/Monotone_cubic_interpolation
- Monotone Convex
- If your bank is using the Caps and Floors functionality, we recommend using the Monotone Convex interpolation method. This is because the Caps and Floors functionality relies on forward rate estimates which are sensitive to artifacts within the interpolated curve (kinks).
- https://en.wikipedia.org/wiki/Monotone_cubic_interpolation
Table 1. Example yield curve spot rates along with interpolated values
| Duration | Rate | Piecewise Linear | Monotone Convex |
|---|---|---|---|
| 0 | 0.2980% | 0.2980% | 0.2620% |
| 1 | 0.2640% | 0.2640% | 0.2640% |
| 2 | 0.2680% | 0.2680% | 0.2680% |
| 3 | 0.2820% | 0.2820% | 0.2820% |
| 4 | 0.2900% | 0.2900% | 0.2900% |
| 5 | 0.3010% | 0.3010% | 0.3010% |
| 6 | 0.3070% | 0.3070% | 0.3070% |
| 7 | 0.3260% | 0.3260% | 0.3260% |
| 8 | 0.3390% | 0.3390% | 0.3390% |
| 9 | 0.3540% | 0.3540% | 0.3540% |
| 10 | 0.3760% | 0.3760% | 0.3760% |
| 11 | 0.3900% | 0.3900% | 0.3900% |
| 12 | 0.4070% | 0.4070% | 0.4070% |
| 0.4475% | 0.4385% | ||
| 0.4880% | 0.4820% | ||
| 0.5285% | 0.5293% | ||
| 0.5690% | 0.5744% | ||
| 0.6095% | 0.6144% | ||
| 18 | 0.6500% | 0.6500% | 0.6500% |
| 0.6802% | 0.6818% | ||
| 0.7103% | 0.7107% | ||
| 0.7405% | 0.7383% | ||
| 0.7707% | 0.7666% | ||
| 0.8008% | 0.7970% | ||
| 24 | 0.8310% | 0.8310% | 0.8310% |
| 0.8707% | 0.8683% | ||
| 0.9103% | 0.9074% | ||
| 0.9500% | 0.9476% | ||
| 0.9897% | 0.9883% | ||
| 1.0293% | 1.0289% |
Graphical differences between methods
The example image below shows the yield curve spot rates (blue markers) along with the two interpolation methods. All of the interpolated lines pass through each and every data point. However, between the data points, there can be slight differences between the methods (see inset). Although slight, these differences can impact the monthly forward rates used within PrecisionLender.
All other interpolations used throughout PL (including Liquidity Curve, Obligor Loss and Obligor Capital Rates) are calculated using the piecewise linear method.
More Information about the math behind these interpolation methods
- Methods for constructing a Yield Curve (Hagan & West)
- A Brief Comparison of Interpolation Methods for Yield Curve Construction