Vanna-Volga

[Duncankhtan]

1) Implied volatility based on the Vanna-Volga model :
VV-Premium = BS-Premium + W_rr * (Smile-RR-Premium - BS-RR-Premium) + W_bf * (Smile-BF-Premium - BS-BF-Premium)

In the above equation, the BS-Premium is typically set using the ATM vol. Therefore, can we have an implied volatility BASED on the Vanna-Volga model? Does it exist?

 

[financeguy]

1) Implied volatility based on the Vanna-Volga model :
VV-Premium = BS-Premium + W_rr * (Smile-RR-Premium - BS-RR-Premium) + W_bf * (Smile-BF-Premium - BS-BF-Premium)

In the above equation, the BS-Premium is typically set using the ATM vol. Therefore, can we have an implied volatility BASED on the Vanna-Volga model? Does it exist?

Well, no, and the reason is basically because we're missing why we use a vanna-volga model to begin with. The vanna-volga model (badly) prices exotics which need to incorporate the full volatility smile rather than one ATM volatility. The smile is roughly incorporated by the premium of the RR and the BF. Exotics themselves can never imply just one volatility number. If you imagine that you observe an exotics price in the market and try to fit it to the vanna-volga methodology, you just end up with a particular RR and BF that may or most likely may not fit the actual vanilla smile, so you just end up with nothing. The vanilla RR and BF that trade more liquidly in the market will produce a particular exotic's price, never the other way around.

 

[dmv]

1) Implied volatility based on the Vanna-Volga model :
VV-Premium = BS-Premium + W_rr * (Smile-RR-Premium - BS-RR-Premium) + W_bf * (Smile-BF-Premium - BS-BF-Premium)

In the above equation, the BS-Premium is typically set using the ATM vol. Therefore, can we have an implied volatility BASED on the Vanna-Volga model? Does it exist?

i am not sure i got you point. but it just a matter of calculation: BS prem -> ImpVol BS (via impvol calculator) , VV-rem -> ImpVol VV (again via impvol calc). You definitely can get a number, what`s the question?