Vanilla options are quoted in volatility terms.

For this to work, both counterparties have first to agree on the values of the inputs to the BS equation (namely forward/IR).

The volatility one must plug into the BS formula to get the true market price of a vanilla option is called the implied volatility. 


In liquid markets, brokers will quote fairly tight two way prices for vanilla options at several strikes. 


Strike Dependence: Skew/Smile

In BS --> single constant volatility for the stochastic process followed by the spot --> options with different strikes would have same volatility --> flat skew. 

Reality --> not at all the case --> volatilities for strikes that are far ITM or OTM are typically higher than the ATM volatility. 


In FX markets --> IV curve usually quite symmetrical around ATM strike --> smile shape. 

In Equity and IR markets --> IV curve is often far from being symmetrical, but heavily skewed in one direction --> skew. 


Markets determine vanilla prices, which in turn determine IVs. 


Time dependence: Term Structure

IV for a given contract also depends on its expiry date T --> IV term structure. 



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