I didn't read that paper (yet)... but, are we discussing skew/smile here? And the reasons for it?
I remember once in Uni, my professor was skeptical about skew/smile... but then when I started in options trading it all made perfect sense.
You can't put everything down on volatility and use that as a single input. That's why Black&Scholes model has to be adapted to be workable in options trading.
IMO skew exists purely because of supply and demand. If an OTM costs 1/3 of ATM, you can buy a lot more insurance for a lot cheaper... so more demand. Also, puts are more expensive because market moves down a lot faster/panic down. And... the market is always net-long in stocks. Market moves up, net everybody wins... market down: net everybody loses. Therefore more demand for OTM puts than OTM calls.
This skew will invert to OTM calls in case of highly likely takeover risk.
As a market maker, you can sell some 'expensive' puts... and buy a shitload of very low value DOTM puts to lower your 'haircut'/downward risk.... say 50% down and vol spike...
In practice it makes sense....