I've been trying to understand the skew I see when looking at the skew of SPX. Here is a snapshot today from thinkorswim. I understand why IV increases for ITM puts -- namely because there is a negative correlation between volatility and moves of the underlying. But I don't understand why the OTM puts IV increase with strike or why the ITM calls IV increase with strike.
I've been studying the different models that give rise to skew. For example:
Local volatility models (e.g. Derman papers)
- Riding on a Smile
- Regimes of Volatility
- The Local Volatility Surface
I understand the increased IV on the left, but it is not obvious to me how these models explain the right portion of the plot above.
The skew plots seem to say that volatility is inversely correlated with underlying moves for a while, but after a "big" move, that correlation (between volatility and underlying price) changes to positive. Is that the correct interpretation? Is this explained by the mean reverting nature of the stochastic volatility in the Heston model?