So an option on UVXY, a leveraged ETP on whatever it is -- index? futures? -- would be a what-order derivative? Fourth-order?
You can take d(NAV of ETF)/d(Underlying Index) to be the delta of an ETF to the underlying (just like a Greek). In general I don't think that it is necessarily incorrect to think of ETFs (and especially ETNs) as derivatives (in the finance sense) and they have pretty well defined derivatives (in the math sense as above).
Just wanted to add that I read that Reuters link. I get the whole "real wealth/asset" argument. But to be honest it feels very synthetic. In practice, owning an ETP has real exposure to the index that can be (nearly) perfectly offset by other ETPs with similar indices. There are real reasons that relationship to the index must hold. As we move into more statistical relationships I'd find "derivative" to be a bit too specific.
Not really what I'm looking for. Just whether I can say UVXY options are third or fourth order derivatives, in whatever sense, math, stat or financial.
How about this? If we assume that saying UVXY is a "derivative" of the VIX index: SPX components (stocks) ---> SPX index ---> SPX options ---> VIX index ---> UVXY (holds VX futures and potentially VIX swaps) The "--->" operator is effectively "is related to".
"A derivative is a contract between two or more parties whose value is based on an agreed-upon underlying financial asset (like a security) or set of assets (like an index). Common underlying instruments include bonds, commodities, currencies, interest rates, market indexes, and stocks." Investopedia. ETFs are not contracts between two parties. If they were, then so are individual stocks.
The reason I'd allow UVXY to be considered a derivative is because the ETN derives its value from the value of a futures contract (the VIX). If it determined it's value directly from the IV of S&P options rather than through a derivative proxy, the waters get muddy again. I wouldn't call it's options an n-order derivative, I'd call them a derivative of a derivative. They mean the same thing mathematically, but in a financial sense a derivative of a derivative makes it far more clear. The SPY isnt a derivative because it represents a basket of stocks. In particular with SPY it's definition makes this clear - The Trust seeks to achieve its investment objective by holding a portfolio of the common stocks that are included in the index (the âPortfolioâ), with the weight of each stock in the Portfolio substantially corresponding to the weight of such stock in the index. It's not deriving its value from anything. It's just a basket that seeks to track the S&P. Maybe if we continue to debate this, we can separate ETNs from ETFs which may help make things more clear.
$SPY does not "derive" its value from $SPX lol Its priced 1/10th the value. That's way different than a true derivative. But the options on $SPY and $SPX derive their value from spot, thus being "derivatives"