I understand the meanings of contango and backwardation, but I'm trying to better understand the theory behind what creates each. For future readers of this question, here are the examples from the CME website:
I have the following questions about the theory behind these two phenomena:
- Since contracts on physical goods have associated costs, it makes sense that the term structure curve would be upward sloping. Since there is no cost associated with delivery for the VIX and contango is considered to exist in healthy markets, is the upward slope simply accounting for the greater potential for the market to become unhealthy over longer periods of time?
- In periods of backwardation, does the existence of historical mean reversion in the VIX cause later contracts to be cheaper than near-term contracts (i.e., mean reversion is the driving factor behind the slopes in both contango and backwardation)?
- Is there a true default state? Would it be a straight line or would it be contango? If contango, is there an established formula that describes contango for VIX purposes, maybe a log curve?
I'm mainly interested in the last question. I'd like to use the term structure as inputs to a machine learning model, but due to the variability in days to expiry, I think it will require some kind of preprocessing. Understanding how a given term structure relates to the default, assuming there is one, will help to determine how to go about that.