Forums  > Pricing & Modelling  > Extrapolating Vol Smile using Lee's Moment Formula  
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Joined: Nov 2020
Posted: 2020-11-11 22:30
Hi all,

I've been trying to use Roger Lee's Moment formula to extrapolate vol smiles. I'm not sure where exactly at what point I'm mistaken, any input is appreciated.

The behavior of the smile as |k| grows is asymptotically bound by a function of log strike k, with some factor beta. I am trying to find some value for beta by plugging in strike, price, and tte into this function.

However, the value for beta changes, and is highly sensitive to the strike of the outermost option. As k approaches 0, beta grows to infinity. In the parametric models I tested (Merton and Heston), it always tapered off as abs(k) -> inf, so there is some 'correct' asymptotic value, but it seems there is no way of determining it from observations.

What am I missing here?


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