I suppose that when you say the historical distribution of log returns, you mean without regard to phase of the bubble cycle. Right?
Correct.
If that is what you did, then perhaps by analyzing each of the previous bubbles you could obtain 10 deciles by partitioning each bubble. Then you could run ten times your existing simulation on each of the 10 decile's distribution.
My own projection of future bitcoin price possibilities heavily depends upon guessing where we are in the bubble cycle. Because I think we are near a bottom, I expect much higher prices this summer as a result.
I can think of a complication or two fitting the deciles, so if that is something that you have no interest in doing, then I have the data to perform a stochastic monte carlo simulation myself.
Not entirely sure what you mean, but in my current (mis-)interpretation of it, I'm not sure it would be a very useful exercise, since I don't consider bubbles to be so predictable and/or uniform. I would be more inclined to consider that a Monte Carlo simulation based on historical data takes on an appropriate amount of bubblyness, which, when averaged out over 50k simulated price paths, are generally smoothed out. If you look at a single generated price path, you clearly see bubbles etc. with characteristics similar to what we have seen historically -- but if you generate 50k paths and summarize them, then the bubbles disappear and the general trend remains. That was kind of the point, and I sidestep any personal opinions on where we are in "the bubble".
Nice. Another refinement might be to take a vol trend line and scale log returns accordingly.
Scale how? And where can I find reliable and representative numbers for volume? In this market, I'm very skeptical to volume figures: I believe the exchanges reflect the general price quite well, but I don't believe the volume on the exchanges is representative for volume traded in total.
