I've been trying to figure this paradox out for a while, buying a few strikes at a couple timeframes. Rising market volatility causes the underlying UVXY to rise, which is a factor causing puts to decline. However, increasing volatility of UVXY is a factor causing both puts and calls to increase in value.
My results are confounding. On a daily basis, some of my puts will be up and some will be down, as quoted based on bid prices. There are two reasons for this:
1) Bid-ask spreads expand and contract unpredictably. One day it might be a 4 cent spread and the next day a 15 cent spread. If your quote is the bid price, your quote reflects a lot of this noise.
2) For a shorter-duration put, the movement of the underlying will have a bigger effect. For a longer-duration put, the change in UVXY's volatility will have a bigger effect. The longer-duration puts offer a "smoother ride" because their decline in response to a UVXY spike is offset to a greater degree by an increase in UVXY's implied volatility. For the same reason, buying UVXY puts right after a big volatility move might disappoint, because the decline in implied volatility when things return to normal will offset much of the gains from UVXY's decline. Thus, I view volatility events as a safer time to buy puts, not a home run opportunity.
I'm not in this trade yet. I'm waiting for the 2020's to come out. But I've been watching it intently for the last few days. The ask for the near ATM 15 strike for the 2019's yesterday bounced between 9.50 and 9.55 all day long. Today, nearly a dollar higher on UVXY's ticker today, the ask was pretty much stuck at 9.55, with only a few brief departures back to 9.50. The swings in the bid, on both days, was much larger, about 35 cents or so.
With a ~$1 move in the underlying, I was understandably a bit surprised to see so little movement in the bid/ask from one day to the next. Sure, 2 days is (admittedly) statistically a tiny sample set, but it seemed as if the VIX was being used in the implied volatility part of the pricing mechanism, rather than the implied volatility of UVXY itself. ??
Even more anecdotally, yesterday, after a quick sharp drop in UVXY, the 9.40 bids for the same put literally evaporated into thin air, instantly, with no trades, only to be replaced by a 9.20 bid; which is exactly the opposite of what I would expect if the VIX were being used to price the options. Confounding indeed.