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This is a big industry, but here are some alternatives(as usual, the best choice depends on purpose and desired accuracy): Fit a quadratic in delta space: $\sigma_{\Delta}=a + b \left( \Delta - \Delta_{ATM} \right) + c \left( \Delta - \Delta_{ATM} \right)^2$. When you have fitted this equation, you can input delta, and the function will return ...

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First off, there are different types of moneyness one can use when constructing a volatility surface. Each have their own advantages. Absolute-moneyness: using absolute spot-strike comparison as a measure of moneyness. ATM would correspond with S=K. This has a simplistic interpretation when looking at option payoff diagrams at maturity. Simple-moneyness: ...

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If you use constant strike, the moneyness changes as the underlying changes. Out of the money equity options tend to trade at a premium to at the money options (smiles/skew). Therefore, the moneyness is used to take into account the movement of the underlying. Yes, if you are trying to price an option with a strike whose moneyness is in between the ...

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In the end I found that fitting a SABR smile to each tenor (borrowing a result from this answer) was sufficient to build a local vol surface that was smooth and well-behaved enough to build a variance surface worked nicely. I also fitted a Heston model to it, and the two surfaces do look fairly similar. Here is the final code and the fits generated (the long ...

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I tried something along these lines in Quantlib python a few weeks ago. Slightly more simple compared to your approach I think: start with a standard delta quote convention for FX vols (10D puts, 25D puts,ATM,25D call, 10D call) calculate the moneyness of the options to obtain the strike set (this will be a large strike set since each option maturity will ...

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See the paper "FX Volatility Smile Construction, Dimitri Reiswich and Uwe Wystup" http://janroman.dhis.org/finance/FX/FX%20Volatility%20Smile.pdf for a comprehensive construction of the FX volatility surface, and in particular converting deltas into strikes. In particular beware that even the notion of ATM may have a different meaning depending on the ...

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I find Dimitri Reiswich's Ph.D. thesis quite useful when it comes to FX smile construction and market conventions. Section 3.3 is on vanna/volga method. Also have a look at Uwe Wystup's book, especially Section 3.1 "The Trader's Rule of Thump". References Reiswich, Dimitri (2010) "The Foreign Exchange Volatility Surface", Ph.D. Dissertation, Frankfurt ...

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Ok, I did some investigations, asked around and got some answers to most of my questions. Since it might be of general interest for other people I present my findings here. How to transfer market data (option prices) from the real world to the simplified zero rate economy (used in the article by J. Andreasen, B. Huge) back and forth. We have an underlying ...

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A cubic polynomial curvature would be the most simple one.Otherwise,many practitioners are actually using a Gaussian process interpolation,which is more sophisticated.

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As explained in the chapter 4.4 of I. Clark, you can estimate the weights by using the typical trading volumes. You can give more weight for dates with bigger trading volume which is logical.

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See https://en.wikipedia.org/wiki/Foreign_exchange_date_conventions for details. In summary expiry = T+tenor for weekly tenors and expiry = ((T+2)+tenor)-2 for monthly and yearly tenors, with all the appropriate business day adjustments.

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