# Is the volatility smile a thing of the past?

Looking for example at this image from bloomberg of the OMX volatility surface, there is only a faint resemble of a smile at the shortest tenors that quickly dissipates as maturity is increased. I find that this is true for all equity surfaces. It seems there is just a very distinct skew, where the implied volatility is higher for lower strike values. Looking at it from the perspective that people value downside protection this pattern makes sense to me, since high demand for OTM puts would make them more expensive and increase the IV, but then why was the smile ever a thing (assuming that it is in face gone)?

• Just a comment: I think the expression 'smile', as in: a nearly symmetrical shape with a 'trough' in the middle section, always relates to specific markets, e.g. FX markets. Especially for large Stock Market Indices, a 'smile' was never the thing, it was always rather a 'smirk' or whatever you want to call it: IVols are rather higher for OTM puts and decrease towards ITM calls. – Kermittfrog Oct 22 '20 at 13:49
• @kermittfrog I think you mean "otm calls" – will Oct 25 '20 at 12:53
• Yes. Thanks. I meant OTM calls – Kermittfrog Oct 25 '20 at 13:34

In equity indexes the skew will be more pronounced than in the individual stocks that make up the index. The volatility of an index, $$σ$$, is related to the volatility of the components, $$σ_i$$, by: $$σ^2=\sum_{i=1}^N w_i^2 σ_i^2+2\sum_{i=1}^{N-1}\sum_{j>i} w_i w_j ρ_{ij} σ_i σ_j$$ where $$w_i$$ are the component weights and $$ρ_{ij}$$ are the correlations between the components.