I have a swaption that when exercised it has 12 delivery months as a strip, all or nothing. I have the implied volatilites of the options and I have a historical vol of the underlying prices. What is a good starting point to model the volatility of this swaption??
There are numerous models for term structure in commodities, each of which could put a price on your swaption.
Some the classic stuff from the 90s (stochastic convenience yield, Gabillon etc) might be a starting point.
The first thing I would do is inspect the shape of the vol term structure and see if that could be easily fit from any of the models.
Is it a standard backwardation? Is it humped?
Is it even reliable data with decent liquidity for each month ? Is the magnitude of the monthly term structure excessive ?
If your chosen model describes that well it’s swaption price will be believable.
Often the liquidity of the underlying products can be a guide. Which is more actively traded? The 12 month future of the calendar swap ?
Depending on the commodity I have seen modelling sophistication vary between libor style models and marking the calendar at the average of the 7th and 8th month.
What is the commodity ?