Understanding skew of SPX - Why does IV of OTM puts increase with strike?

Question

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

• Heston stochastic volatility model

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?

Answer 1

When I saw these curves they seemed very strange to me. I believe it is a data-quality issue.I went to Bloomberg and I retrieved the implied vols for 70 near ATM strikes of the weekly SPX options expiring November 27 2015 (I believe that is the yellow curve in your diagrams i.e. November 4th week). This was today 2015-oct-27 at about 15:00 New York time. As you can see from the table below, the vols are monotonic for both calls and puts, completely unlike the U shape seen in the curve you posted.

27 Nov 15 (31d); IDiv 3.22; R .20; FF 2062.47

 Strike      Call IV      Put IV
 1975   15.950  17.352
 1980   16.484  17.058
 1985   0.000   16.795
 1990   16.175  16.462
 1995   21.817  16.258
 2000   16.235  16.202
 2005   15.485  15.908
 2010   15.730  15.712
 2015   15.887  15.481
 2020   15.250  15.330
 2025   15.148  15.013
 2030   14.812  14.895
 2035   14.701  14.598
 2040   14.341  14.363
 2045   13.884  14.156
 2050   13.916  13.899
 2055   13.774  13.678
 2060   13.465  13.358
 2065   13.217  13.194
 2070   13.041  12.981
 2075   12.724  12.638
 2080   12.560  12.289
 2085   12.307  11.587
 2090   11.977  11.123
 2095   11.737  11.042
 2100   11.606  11.676
 2105   11.426  11.275
 2110   11.146  7.126
 2115   11.081  10.512
 2120   10.891  9.904
 2125   10.755  0.000
 2130   10.574  0.000
 2135   10.489  0.000
 2140   10.370  0.000
 2145   10.243  0.000
 2150   10.324  0.000

Make sure that your IV's are computed from the bid ask midpoint, not the last price (which could be several hours old) and that there is real market activity in the way far out of the money strikes that you are displaying. There was no activity at all today in strikes higher than 2120 (for puts) and very little above 2170 for calls. Those prices (and IV's) may not be meaningful.