Linear interpolation formula
Financial acronyms
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Description and Usage of the Linear Interpolation Formula
The formula below shows how to calculate a value through the process of linear interpolation. Linear interpolation is a mathematical process that estimates a value by calculating an average of two known, surrounding values. Linear interpolation is frequently employed in finance, for example, to estimate the yield or price of financial instruments, especially when dealing with irregular time intervals or missing data points in a time series.
Linear Interpolation Formula
Symbols
Practical example for the use of linear interpolation
Scenario
Let's consider an example from finance where linear interpolation is used to estimate the yield of a financial instrument between two known data points. Suppose you have the following data on the yield of bonds for different maturities:
- For a maturity of 2 years (x1), the yield is 4% (y1)
- For a maturity of 5 years (x2), the yield is 5.5% (y2)
Calculation
Now, you want to estimate the yield for a bond with a maturity of 3 years (yi) using linear interpolation. Using the formula above, the calculation steps are as follows:
yi = 0.04 + (0.055 − 0.04) × ((3 − 2) ÷ (5 − 2))
yi = 0.04 + 0.015 × ( 1 ÷ 3 )
yi = 0.04 + 0.005
yi = 0.045
Interpretation
Using linear interpolation, the estimated yield for a bond with a maturity of 3 years is 4.5%. This method provides an interpolated yield based on the linear relationship between known data points.