Tradable information from BS Implied volatility

Question

These are two follow up questions to:

Implied volatility as price transform

1. I understand that the BS model is used as a 'Blackbox' that takes a market price and maps it in a 1to1 fashion to a 'BS implied volatility'. What I don't understand is how there is any actionable information in that IV number given that everybody knows that most assumptions of BS do not hold. Yes, I know it is well understood and a bad model is better than no model. But let's say in a different universe somebody might have come up with a different model $\phi$ that shares the characteristics that make BS so popular. Now $\phi$ gives different IVs and hence also different actionable information. So how come traders actually use that information in trading if itstems from an 'arbitrary' Blackbox?
2. The second question is based on the following slide of a talk given by P. Staneski, an MD quant at Credit Suisse:

   In the world of Black-Scholes, implied volatility is the expected value of future realized volatility because they are both constants!

   • Even if we allow for stochastic volatility, given the other assumptions implied volatility is the expected value of future realized volatility.

   In the real world, none of the assumptions are true (some being more false than others, particularly the constancy of vol and GBM).

   • The market gives us the price of an option, which “embeds” all the imperfections traders must deal with.

   • There is only one degree of freedom in the B-S model, namely, the volatility input, which must be “forced” to match the model to the market.

   Implied volatility is thus a lot more than expected volatility!

If as he claims IV is a lot more than expected volatility, how can a trader sensibly use that information in trading? Very often, I saw things like (in summary) "If the implied vol is 20 and you think volatility is gonna realise at 18, you just go short vol by selling a call/put and delta hedge it, thereby making money if you are right". Well, what if 5 of my 20 implied vol actually stems from the inaccuracy of the BS model and is not 'priced in expected realised variance'?

Answer 1

Actually my interpretation of the quote is that implied vol is DISCONNECTED from realized vol, because of the different information it contains, hence his reference to the market, and all the imperfections. Implied vol can be considered a consensus expectation of future volatility AS OF any given time, but in practices consensus expectation and fair estimator are two different things.

Answer 2

1. "So how come traders actually use that information in trading if itstems from an 'arbitrary' Blackbox?". You make a bet on realized vol via delta-neutral option position. if you believe that realized vol will be different from IV of BS (or your another model) than do exactly what you mention in question 2. if IV is too high: sell option, delta-hedge with underlying and collect difference either from IV change or from delta-rehedging (gamma trade).

2. CS guy is right and you should think about his statement in broader sense. Say, real distribution of returns is leptokurtic with fat tails. What does it mean? it means that at some of time may occur some event that is extremely rare from point of view of normal distrib. and such extreme events may occur much more frequently than normal distrib suggests. So how can you incorporate this observation in option price? only through one input - IV. you simple increase IV. and if for example your you price your option as realized vol=20% + fat tails events fears=2% total IV=22% it does not matter if fat tail event happens or not, any case you have difference IV=22% vs realized=20% right before the trade and if you sell the option you will earn you 2% of difference if gamma let you. once again - it does not matter why IV is so high (you should not care about what imperfections seller input into IV), the only thing that matters is difference between IV and realized vol