I have posted a paper on SSRN with the title:"Stochastic Model For The Price Of Bitcoin". It is available at this link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3243011
The abstract of the paper:
Quote
This paper analyses the price of bitcoin to show that the price-difficulty ratio can be modelled using a lognormal distribution. Building on this result it is shown that a stochastic model for bitcoin can be constructed that uses a model similar to the stochastic model for stocks, but with the growth of difficulty as the drift. Further, certain constraints on the price of bitcoin are derived that exist after the introduction of short futures. These show that bitcoin should trade below the cost of production, where the cost of production is the sum of the electricity cost and the cost due to financing. Based on very limited recent price information it seems that a floor might exist at the cost due to electricity. It is also shown that these levels will grow with a growth in difficulty. This would imply that, should the difficulty of bitcoin keep rising, that the price of bitcoin will also keep rising while staying within a range that also keeps rising. Finally, it will be explained that the percentage that the electricity cost makes up as part of the production cost will rise as the rewards for mining are reduced, thus possibly shrinking the trading range of bitcoin and reducing its volatility over time.
Comments and suggestions are welcome.