These are two follow up questions to:
- 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?
- 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'?