Plan

To start:
  1. (Done) Plot the IV difference and S&P 500 index in the same graph. Use only deep-out-of-the money and out-of-the money  puts and calls on sentiment. Do not worry about at-the-money or (deep)in-the-money options.)
  2. (Done) Plot the IV difference and the VIX in the same graph.
  3. (Done) The same for short-term maturity options.
  4. (Done) Calculate correlations between the differences in IV estimated from  deep-out-of-the money and out-of-the money  puts and calls on sentiment.
  5. (Done) The same with short maturity options.
  6. The same with long maturity options - probably 100 to 360 days.
  7. Regressions: to think about. I like the approach of Whaley (2008)
  8. Trading strategy