Did anyone derived the local volatility from implied volatilites using the spot prices in the moneyness?Also, using two different year fracs for Vol Days and Carry?
I´ve done it but its highly unstable even when I use a parametric model to fit the smile( Something like SVI...)
Thanks
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Re: Local Volatility
Not pretty clear with your question. Do you mean the functional form of local vol in terms of IV? And what do you mean by 'using two different year fracs for Vol Days and Carry?'
Re: Local Volatility
I mean if you have two different settlement calendars.
One for you Risk Free and another one for the Exchange which your underlying trades, the case for Brazil for instance.
so in your derivation the Time to maturity w.r.t to the forward might be different then the Time associate with the volatility.
One for you Risk Free and another one for the Exchange which your underlying trades, the case for Brazil for instance.
so in your derivation the Time to maturity w.r.t to the forward might be different then the Time associate with the volatility.
Re: Local Volatility
It is common in option modeling to differentiate between diffusion or volatility time, and the forward period for the underlying. The instant you execute an option trade you are exposed to price movements in the underlying even though a spot trade in the underlying made at the same time hasn’t yet settled. See where this is going? A settlement lag in the underlying may interact with its date roll convention such that the forward period may not coincide with the volatility exposure period. Any decent textbook should show this distinction.
Re: Local Volatility
The moment you trade the option you have to manage the risks in your book. The differences between trade and settlement usually are the same when you open and close your position so the number of days of the "carry" won´t change, just make sure to account for it.It is common in option modeling to differentiate between diffusion or volatility time, and the forward period for the underlying. The instant you execute an option trade you are exposed to price movements in the underlying even though a spot trade in the underlying made at the same time hasn’t yet settled. See where this is going? A settlement lag in the underlying may interact with its date roll convention such that the forward period may not coincide with the volatility exposure period. Any decent textbook should show this distinction.
The forward days and volatility period mismatch is exactly my point and I look everywhere but I haven´t found a way to deal with that.