Several people already pointed out that what is most frequently used as a model for prices is precisely the log random walk. This should have been obvious since no asset can have a negative price, and it is known that the long-term probability of the one-dimensional random walk reaching any specified point (such as zero) is 1 (same for 2D, not so in 3+ D) - this part of how casinos make money.
It is very easy to spot why the random walk model doesn’t make sense for prices, just take the sentence that says “If today’s Bitcoin price is $1000, then tomorrow’s price is as likely to be $900 as it is to be $1100.” Now if the normal random walk model were true, then you could also have said that the price is as likely to deviate by +X as it is by -X for any X. Now take X=1000: is it as likely to cost $0 as it is to cost $2000?
can’t dispute the conclusion but I object to the argument.
Because, the argument doesn’t apply to this model: “Probabilities are calculated from a random walk, except for large unlikely changes, or changes when the price is near zero.”
Approximate models always have a range of applicability. Showing that the model gives absurd results outside the range of applicability for which it’s intended doesn’t mean much.
Several people already pointed out that what is most frequently used as a model for prices is precisely the log random walk. This should have been obvious since no asset can have a negative price, and it is known that the long-term probability of the one-dimensional random walk reaching any specified point (such as zero) is 1 (same for 2D, not so in 3+ D) - this part of how casinos make money.
It is very easy to spot why the random walk model doesn’t make sense for prices, just take the sentence that says “If today’s Bitcoin price is $1000, then tomorrow’s price is as likely to be $900 as it is to be $1100.” Now if the normal random walk model were true, then you could also have said that the price is as likely to deviate by +X as it is by -X for any X. Now take X=1000: is it as likely to cost $0 as it is to cost $2000?
can’t dispute the conclusion but I object to the argument.
Because, the argument doesn’t apply to this model: “Probabilities are calculated from a random walk, except for large unlikely changes, or changes when the price is near zero.”
Approximate models always have a range of applicability. Showing that the model gives absurd results outside the range of applicability for which it’s intended doesn’t mean much.