Full Disclaimer: I first asked this question on Bitcoin.SE, however I feel like my question is more relevant to this site as there would be wider knowledge and insight of some better sources or studies available. Additionally, this site would offer better responses into the modelling and hedging techniques involved in this new asset class. There was a link to a podcast in the comment section of my question on Bitcoin.SE, but it didn't seem to answer what I was looking for.

Some research I have done has highlighted how mining has an impact on the performance of certain utility companies. Other closely linked questions have been asked on other sites, but without an answer. The closest study I could find was here, which discussed how energy suppliers could direct surplus output into mining power.

I was wondering if there were any academic papers or studies, that have discussed the existence of a model, or a link, between energy markets and Cryptocurrency mining. In particular, is there a hedging-strategy that miners could use such that increasing electricity costs or decreasing Cryptocurrency prices are mitigated for.

I have come up with a simplified problem, which a miner (Bob) faces: Should he mine or not?

Suppose there is a miner, Bob, who's mining equipment produces a fixed hashrate and is not a part of any collective mining pool. He mines constantly, drawing electrical power from an outlet. Should Bob produce a valid block that is accepted by the network, he sells the block reward, plus any transactions fees, immediately. The decision, whether Bob should mine or not, depends on the following variables:

  • The spot price of electricity, $I_{t}, t \geq 0$, which follows a stochastic process.
  • The spot price of Bitcoin, $(BTC_{t})_{t \geq 0}$, which follows a stochastic process.
  • The network difficulty, $N_{t}$, which follows a jump process in $[1, 2^{224}]$.
  • The total network hashrate, $H_{t}$, which follows a stochastic process.
  • Block reward, $R_{t}$, which follows a deterministic process.
  • Transaction fee rewards per block, $TX_{t}$.
  • Bob's hash rate, $BHR_{t}$, which decays exponentially.

The event of Bob producing a valid block has probability $\mathbb{P} = \frac{BHR_{t}}{H_{t}}$, as he is competing against the rest of the mining network.

Bob wishes to ensure that in expectation, mining yields a profit. Of course this depends on these aforementioned variables. Bob also wishes to ensure that if mining isn't profitable, given the spot prices of $BTC_{t}$ and $I_{t}$, he could hedge himself against this risk by using any electricity market derivatives, or cryptocurrency market derivatives.

Or, if it would still not be profitable to mine, he could lease his computational power as cloud services for a fixed, deterministic rate per given time period, to ensure he earns a rate of return on his machinery. Conversely, he could choose to mine an entirely different cryptocurrency that would yield a profit, of course, in expectation.

This way, miners could have more certainty when mining, using derivative products to hedge themselves against sudden drops in the price of Bitcoin, or sudden increases in the cost of electricity. I was wondering if any such papers or studies exist, or how such a hedging strategy could be formulated. I feel like the dynamics would be interesting to study.

  • $\begingroup$ Nice question; food for thought! In my place, we pay for electricity at fixed prices per kWh for all practical purposes. I understand that you think in a larger quasi-industrial setting, no? $\endgroup$ Commented Apr 14, 2021 at 17:00
  • $\begingroup$ Yes I was thinking of something just along those lines! For the sake of the problem sketch I just stated that it was a stochastic process, I'm sure more accurate representations exist. $\endgroup$ Commented Apr 14, 2021 at 17:04
  • $\begingroup$ Why would his hash rate decay exponentially? $\endgroup$
    – Bob Jansen
    Commented Apr 14, 2021 at 17:13
  • $\begingroup$ The degradation and depreciation of his hardware due to constant use. $\endgroup$ Commented Apr 14, 2021 at 17:21


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