# When Fitting Implied Vol in, implied vol=ax²+bx+c, why is better to use moneyness than delta as independent variable?

I am trying to construct a smile curve using Option data, I can either interpolate implied vol vs delta or implied vol vs moneyness.

## 1 Answer

What I have seen in papers such as Christoffersen, Heston and Jacobs (2009) where they look into a two-factor model of volatility is a quadratic polynomial in BOTH moneyness and maturity.

I would assume that the advantage of using this approach is that you get a structured volatility surface using observed variables. Beyond the problem of having to estimate the derivative of a pricing function you do not have, your delta likely will depend on some measure of volatility under Q.

• thanks, Stephane thats what I thought. There is a well known quadratic relationship btw volatility and moneyness/maturity. I guess the best way to proceed is interpolate in the moneyness and then numerically calcuate the deltas. – william lee Mar 30 '20 at 23:49