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 three interpolation methods when dealing with yield curves:

interpolation method drop down box

Piecewise Linear
A simple line is drawn between each data point on the curve
https://en.wikipedia.org/wiki/Linear_interpolation
Cubic Spline
https://en.wikipedia.org/wiki/Cubic_Hermite_spline
Monotone Convex
https://en.wikipedia.org/wiki/Monotone_cubic_interpolation
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).

Table 1. Example yield curve spot rates along with interpolated values:

Duration Rate Piecewise Linear Cubic Spline Monotone Convex
0 0.2980% 0.2980% 0.2980% 0.2620%
1 0.2640% 0.2640% 0.2640% 0.2640%
2 0.2680% 0.2680% 0.2680% 0.2680%
3 0.2820% 0.2820% 0.2820% 0.2820%
4 0.2900% 0.2900% 0.2900% 0.2900%
5 0.3010% 0.3010% 0.3010% 0.3010%
6 0.3070% 0.3070% 0.3070% 0.3070%
7 0.3260% 0.3260% 0.3260% 0.3260%
8 0.3390% 0.3390% 0.3390% 0.3390%
9 0.3540% 0.3540% 0.3540% 0.3540%
10 0.3760% 0.3760% 0.3760% 0.3760%
11 0.3900% 0.3900% 0.3900% 0.3900%
12 0.4070% 0.4070% 0.4070% 0.4070%
    0.4475% 0.4349% 0.4385%
    0.4880% 0.4721% 0.4820%
    0.5285% 0.5155% 0.5293%
    0.5690% 0.5618% 0.5744%
    0.6095% 0.6077% 0.6144%
18 0.6500% 0.6500% 0.6500% 0.6500%
    0.6802% 0.6863% 0.6818%
    0.7103% 0.7177% 0.7107%
    0.7405% 0.7459% 0.7383%
    0.7707% 0.7730% 0.7666%
    0.8008% 0.8007% 0.7970%
24 0.8310% 0.8310% 0.8310% 0.8310%
    0.8707% 0.8652% 0.8683%
    0.9103% 0.9029% 0.9074%
    0.9500% 0.9431% 0.9476%
    0.9897% 0.9848% 0.9883%
    1.0293% 1.0271% 1.0289%

 

Graphical differences between methods

The example image below shows the yield curve spot rates (blue markers) along with the three 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.

Cinterpolate.PNG

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

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