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That would be unlikely, as uncertainty will always exist in the market. Also, negative oil futures was largely caused by the rollover of contracts. Since it's not a commodity to take physically, there won't be a lack of demand like oil. It would be interesting to think about however.
CatchaRid
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VIX being a function of SP options price changes would make me say no, VIX cannot go negative. Also, the comparison to Oil is skewed. VIX does not have a dollar value or price. It is a measurement.
Ian_Carsen
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Great video! Glad I'm following you when pop into the notifications every once in awhile