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.