Editing Volatility smile (section)

===Formula===

: <math>\operatorname{Call}x = \mathrm{ATM} + 0.5\operatorname{RR}x + \operatorname{Fly}x</math>

: <math>\operatorname{Put}x = \mathrm{ATM} - 0.5 \operatorname{RR}x + \operatorname{Fly}x</math>

where:

* <math>\operatorname{Call}x</math> is the implied volatility at which the ''x''%-delta call is trading in the market
* <math>\operatorname{Put}x</math> is the implied volatility of the ''x''%-delta put
*ATM is the At-The-Money Forward volatility at which ATM Calls and Puts are trading in the market
* <math>\operatorname{RR}x = \operatorname{Call}x - \operatorname{Put}x</math>
* <math>\operatorname{Fly}x = 0.5(\operatorname{Call}x + \operatorname{Put}x) - \mathrm{ATM}</math>

[[Risk reversal]]s are generally quoted as ''x''% delta risk reversal and essentially is Long ''x''% delta call, and short ''x''% delta put.

[[Butterfly (options)|Butterfly]], on the other hand, is a strategy consisting of:
−''y''% delta fly which mean Long ''y''% delta call, Long ''y''% delta put, short one ATM call and short one ATM put (small hat shape).