Vincent Granville wrote:
>The problem is to find the (parametric?) distribution of
>the ratio low/high in connection with Brownian motions.
>The application I have in mind is daily low/high or 52-week
>low/high for any particular stock price.
Brownian motions are usually described as having a
Maxwell distribution (in three dimensions) or a
Rayleigh distribution (in two dimensions). It's not clear
how a daily low/high ratio of stock prices would relate to
either of those distributions, because the domain of the
low/high ratio is from zero to one, whereas the Maxwell and
the Rayleigh distributions both have positive, unbounded
domains.
Another distribution, such as the Dirichlet, might be a
better model.
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