How to measure curvature of a curve using slope?

Question

I am analyzing a financial instrument that has seven prices. The seven prices each have an expiration of 1 month, 2 month, 3 month etc. I would like to measure the curvature of the curve. I know how to easily calculate the slope of the curve, but how do I calculate the curvature? Here is an example of one series:

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Thank you,

Answer 1

For plane curve $y=f(x)$, $$\kappa = \frac{y''}{(1+y'^{2})^{3/2}} $$ For small $h$, $$y'=f'(x) \approx \frac{f(x+h)-f(x-h)}{2h} $$ $$y''=f''(x) \approx \frac{f(x+h)-2f(x)+f(x-h)}{h^{2}} $$