Given that it sounds like nobody has actually run the numbers, is there a reason to suspect that bitcoin prices are best modeled by a uniform random walk on the log scale? If it is modeled instead by a weighted random walk with an appropriate negative drift term the expected value of a BTC tomorrow could be exactly equal to today’s expected value (or more exactly today’s value adjusted for inflation).
Well, rather then modelling the price at time t by exp(B t) were B is a Brownian motion, you could model it by exp(B t—c*t) for some constant c.
On a more basic level instead of saying that after a day the price will be multiplied by either 0.9 or 1.111 with equal probability, you could have the price multiplied by either 0.9 or 1.1 with equal probability. In the later case, the expected value tomorrow is exactly the value today. On the other hand, because 0.9*1.1 < 1, this later process will end up at 0 in the long run almost surely. Then again, this model would probably only work as a first order approximation to the behavior anyway. If bitcoin ever does manage to become a competitive major currency, its volatility would almost have to decrease drastically.
Given that it sounds like nobody has actually run the numbers, is there a reason to suspect that bitcoin prices are best modeled by a uniform random walk on the log scale? If it is modeled instead by a weighted random walk with an appropriate negative drift term the expected value of a BTC tomorrow could be exactly equal to today’s expected value (or more exactly today’s value adjusted for inflation).
How does this “negative drift term” work? What variables are in it?
Well, rather then modelling the price at time t by exp(B t) were B is a Brownian motion, you could model it by exp(B t—c*t) for some constant c.
On a more basic level instead of saying that after a day the price will be multiplied by either 0.9 or 1.111 with equal probability, you could have the price multiplied by either 0.9 or 1.1 with equal probability. In the later case, the expected value tomorrow is exactly the value today. On the other hand, because 0.9*1.1 < 1, this later process will end up at 0 in the long run almost surely. Then again, this model would probably only work as a first order approximation to the behavior anyway. If bitcoin ever does manage to become a competitive major currency, its volatility would almost have to decrease drastically.