Understanding the interpolation technique

Interpolation is a technique used quite frequently in finance. In the following example, we have to find NaN between 2 and 6. The pd.interpolate() function, for a linear interpolation, is used to fill in the two missing values:

>>>import pandas as pd
>>>import numpy as np
>>>x=pd.Series([1,2,np.nan,np.nan,6])
>>>x.interpolate()
0  1.000000
1  2.000000
2  3.333333
3  4.666667
4  6.000000

If the two known points are represented by the coordinates (x0,y0) and (x1,y1), the linear interpolation is the straight line between these two points. For a value x in the interval of (x0,x1), the value y along the straight line is given by the following formula:

Solving this equation for y, which is the unknown value at x, gives the following result:

From the Yahoo! Finance bond page, we can get the following information:

Maturity	Yield	Yesterday	Last Week	Last Month
3 Month	0.05	0.05	0.04	0.03
6 Month	0.08	0.07	0.07...