While the concept of volatility smirk is simple, the pattern itself is unstable. For example, different expiries have different shapes.
And these shapes change across days as well.
One way to keep track of these changes is by fitting a model through the implied volatilities. Here, we fit a parabola (y = ax2 + bx + c). a, the coefficient of strike_pct2, gives a measure of the narrowness/steepness of the smirk.
By sampling the curve and tracking these coefficients, you can begin to form an opinion on what is “normal” vs. a trading opportunity.
Code and charts on github.