pricing exotic options

[Lun]

from wiki, I find the following description

http://en.wikipedia.org/wiki/Volatility_smile

"Modelling the volatility smile is an active area of research in quantitative finance. Typically, a quantitative analyst will calculate the implied volatility from liquid vanilla options and use models of the smile to calculate the price of more exotic options."

my question is how I can use models of the smile to calculate the price of more exotic options ?

Well, are there good books or resources in the internet for this topic ?

Thanks !

 

[Alexei]

Amazon.com: The Volatility Surface: A Practitioner by Jim Gatheral
and
Lecture Notes
and
Modeling the Volatility Smile
by Emanuel Derman
and
IMPLIED VOLATILITY SURFACES AND OPTION PRICES

 

[Lun]

Thank you very much for the resources.

Do you mean that I can replicate the exotic option with static hedging, and use the static replicating portfolio to valuate the exotic option ?

For having a static replicating portfolio, a number of standard options are needed, and that's why a (model for) smile is needed. Am I right ?

If I'm in the wrong direction, pls correct me, thanks !

 

[Lun]

According to the work of Derman, exotic options can be statically replicated by a number of standard options for pricing, but smile is not mentioned in the pricing. I can't see the relationship between exotic option pricing and smile, can anyone help ?

 

[iHateVariance]

smile is captured in the prices of standard options. if ur exotic can be replicated with vanilas then price of the exotic will be equal to the price of replicating portfolio and be smile consistent. in some instances exotic cannot be staticly hedged and would require u to rebalance ur hedges in vanilas giving u exposure to the dynamics of the smile which u might consider modelling