# Looking for a measure of variance of variance?

I was hoping you would be able to help me identify the statistic I am looking for, or point me in the right direction.

Is there a statistical measure that will represent variance of variance (or s.d. of s.d.)? In the graphs attached, is there such a measure that will identify graphs 1 and 2 as similar because variance is pretty constant for all values of x, and show graphs 1 and 2 as different from graph 3 as the variance of graph 3 fluctuates greatly as we change x? I understand that I could split the x axis into bins, calculate the variances of each bin, then calculate the variance of the bin variances but is there a better way that wouldn't involve more decisions to be made (like bin size)?

In quant finance there are several models that incorporate such a concept. For instance, SABR model looks as follows in a simplest form: $$dF_t=\sigma_t \left(F_t\right)^\beta\, dW_t,$$ $$d\sigma_t=\alpha\sigma^{}_t\, dZ_t,$$ were, $$\alpha$$ is the variance of the variance of the changes in rate series $$F_t$$.