I am doing some standard svd calibration to mark market implied vols in difference to a previous volatility surface.
For longer term maturities where there is no market data, I am extrapolating ATM using forward variance which leads to very high moves compared to consensus data. Exact behavior will be: if my last observable vols are peaking down, I will have an amplification of that move before eventually coming back to the init volatility surface thanks to regularization constraints. So I can have small moves on the first 2Y big move on 3Y and small moves again on 5Y.
When there is consensus data available I usually shut down the extrapolation and the results are much better. Have any of you used different methods for extrapolating volatilities ?