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I am trying to extrapolate the vol surface using Gatheral's SVI parametrization. I am working in excel and wrote the levenberg-marquardt algorithm to estimate the parameters of each expiry. This fits each individual skew very well (small squared residuals), however, the term structure of the wings lacks cohesion and does not satisfy the no calendar spread arbitrage conditions.This is a result of the data, however, this will be typical from what I have seen. Could someone recommend an optimization procedure that I can use, to calibrate the whole surface using the SVI parametrization, ensuring the no calendar spread arbitrage condition is satisfied.Appreciate any thoughts. Thanks!