# Intuition behind Implied Volatility Surface

When looking at an implied volatility surface, are there some intuitive conclusions that one can draw from the shape? E.g. the steepness of the wings, the skew etc?

If one for example compares two implied volatility surfaces, are there certain intuitions one could get about the market opinions on the two underlyings, based on the shape?

Perhaps related to your questions is the estimation of RND (risk-neutral density). It is well-known that $$q(x) = e^{rT} \frac{\partial^2 C(K)}{\partial K^2}\bigg|_{K=x} = e^{rT} \frac{\partial^2 P(K)}{\partial K^2}\bigg|_{K=x}$$ Thus, we can infer a risk-neutral density from observed European option prices. However, we need to be careful and first transform a risk-neutral density into a real-world density. Then indeed, you can see what market participants really expect for the market. Policy makers at central banks use this tool. See also Chapter 16 in Taylor (2005).