Implied Volatility

This is a more market-related volatility concept. This takes everything to the next step, taking into account the options market. 

By observing the price of the option, one can back out the σ parameter one has to push into the formula in order to find that price. The market has adjusted for the shortcomings of the BS model and the market-implied distribution is not lognormal anymore. 

However, the beauty of the BS formula is that you can tune your σ parameter such that you match this market price of the option. 


Implied volatility is the wrong number you put in the wrong formula to get the right price   --> "Rebonato". 


Sometimes analysts try to use IV to defer conclusions about market direction. It is very tempting to think that this information is present in the option market, but the motivation for buying an OTM put does not have to be because the buyer is expecting a decrease in the stock price. 


From the trader's point of view, knowing there is a huge interest can bring about two thoughts. 

First, he should increase his price. This is basic feature of supply and demand. 

Second, if the scale of the orders become really big, he might become less comfortable with the risk and he might want a bigger premium for that. 


This clearly means that the IV does not imply anything for the future. There are extensive studies on comparing the realied volatility to the IV. Typically there is a risk premium in the IV --> IV > RV. 



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