Trying to fit variants of SVI (Zeliade method, SSVI etc) to options on futures price data. One of the core ideas of the SVI parameterization is the absence of calendar spread arbitrage.
I think the SVI fitting procedure kind of makes sense in the context of financial futures (where the basis between delivery months is mostly a function of the risk free rate). However, in commodity futures there can be a massive difference in the fundamentals/behavior along the futures curve. E.g. Natural gas in winter vs summer
Examples of fitting SVI to options on futures (see here) seem to build the forward curve using options on futures of different delivery months (because in futures there typically exists one options expiry per futures contract traded, as opposed to equities which have many expiries every month). And parameterizing SVI by penalizing for existence of calendar spread arbitrage and butterfly arbitrage.
So assume we are looking at Natural gas futures options and fitting SVI using March and April natural gas futures options. Delivery of natural gas in March is still considered a "winter" month, whereas delivery of natural gas in April is summer. Does it make sense to assume no calendar spread arbitrage between the March and April expiries (two fundamentally different underlyings) when fitting SVI? If not, then how does one fit surfaces to commodity futures options (perhaps the answer is just only fitting one slice at a time)?