Taylor approximation formula


Taylor approximation formula

We know that when the yield on a bond changes, the bond's price will also change. What investors need to know is by how much. In finance, we often approximate a complex function by other simpler functions. The Taylor approximation formula does this by employing derivatives, that is, rates of change.

Geometrically, the derivative is defined as the slope of a line, that can be measured by the change in the y-coordinate (Price) caused by a one unit change in the x-coordinate (Yield). In mathematical notation, this would be:

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For the purpose of bond analysis, all we need is the general rule for obtaining the derivative of a non-linear function of the form:

[

Hence, we bring down the negative power to multiply ax and then subtract 1 from the power.


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