Finance recognises a derivative as a contract deriving value from the performance of an underlying entity.
Using this perspective, the profit of a widgit making factory is a derivative, because the value is derived from the widget machines cranking out widgets. This is not the way that derivatives are usually represented. Finance usually relates derivatives to underlying entities such as assets, indexes, or interest rates. Derivatives have application to a number of purposes: insurance against price movement, increasing exposure to price movements for speculation, or gaining access to difficult trade assets and markets. The distinction between the indexes, interest rates, and widget machines is very similar to the distinction between proof of work and proof of stake.
Bitcoin is usually represented as being proof of work which is reasonable: agreement is provided by solving a mathematical problem which ensures that the transaction can be trusted in a trustless environment. The proof of work is all in the rapid solution of that mathematical problem. That makes Bitcoin a derivative, in the technical sense, of solving a mathematical problem. True, it is a very narrowly defined problem. But it is, technically, a derivative. Alternately there is proof of stake. Peercoin was the first implementation of proof of stake where agreement is provided by owning sufficient tokens to participate in validation.
The only transactions taking place are the recording of exchanges.
Fundamentally, both proof of stake and proof of work derive their value from some underlying thing. Yet, when you examine the situation more critically it becomes obvious that both derive their value from the amount of electricity used. Cryptocurrencies are simply electricity derivatives. This creates a genuine problem for the value of some cryptocurrencies because the electricity does not come with the Cryptocurrency. Unless there is some evidence of useful employment of the underlying asset - the electricity - then there are grounds for profound doubt about the value of a cryptocurrency.
Unless a cryptocurrency has some tangible value that can be exchanged there is very little point in having more than one cryptocurrency. Once there is more than one cryptocurrency it becomes a matter of showing genuine value - other than electricity usage - is attached to the coin. For DOGE there is a value in the community support for, say, the Jamaican Bobsleigh Team or NASCAR. The value exchange is, clearly, transitory and based in social activities. But, the value is there. Without that tangible value, the cryptocurrency is nothing more than a derivative of fiat.
Which is a problem that is not solved by bouncing between proof of stake and proof of work. What it requires is what DOGE appears to have blundered into: a combination of proof of stake and of proof of work. DOGE moves between a community that has community values which DOGE mediates the realisation of. This is actually quite close - albeit not technically - to the supposed mediation provided by many Non Fungible Tokens. The most important question becomes: what contract does this crypto form with the underlying asset. Which needs an understanding of the underlying assets and the contract being formed.
