Volatility surface fitting, interpolation and extension from sparse data

External question — Quantitative Finance Stack Exchange Author: user13655 Original post: https://quant.stackexchange.com/questions/43493 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. There are some nice papers about constrained spline fitting essentially giving you a smoothing and arb free surface. I am focusing on the oil market here: The market is essentially split in a very liquid screen based front part (about 1yr out) and a broker based back end. Far end atm prices are fairly easy to get/guess, but the skew less so. Skew information comes mainly through spreads, ratios and fences giving you spares data there. I was wondering if there is an elegant way to make use of that data? This is purely about vanillas, so no fancy vol dynamic required. Intuitively, you'd probably have to force a fit using stylised facts like a flattening skew and smoothness constraints. Maybe a two step procedure would be best? Any suggestions welcome. Thank you