http://en.wikipedia.org/wiki/Black%E2%80%93Scholes

Black-Scholes model assumes securities prices follow a log-normal distribution, so the logarithm of prices follow a normal distribution.

Let's say Y = log(Price). Y follows a normal distribution.

So if I take the arithmetic mean of Y as an estimate for the mean, and it's for example 1.2 and the current Y is 1. So I know that for example P([1.1, +∞[) is higher than P(]0, 0.9]). So in this example, if I bought that security at the price whose logarithm is 1 (price = e^1) and I took profit if it reached the price whose logarithm is 1.1 (e^1.1) and closed with a loss if it reached e^0.9, I'd win in the long term.

I'm just a begginner in statistics, just started studying statistics this year. But I see many problems why this wouldn't work:

- First of all I don't know if prices really follow a log-normal distribution, I haven't found much information about this. I only know this is assumed in the black-scholes model, and that model is used to price options.

- The distribution function would change in time. As time passes, the mean would vary. Because of this I don't know if I can use this distribution that doesn't consider time.

If anyone knows statistics and probability theory here, what do you think?

Black-Scholes model assumes securities prices follow a log-normal distribution, so the logarithm of prices follow a normal distribution.

Let's say Y = log(Price). Y follows a normal distribution.

So if I take the arithmetic mean of Y as an estimate for the mean, and it's for example 1.2 and the current Y is 1. So I know that for example P([1.1, +∞[) is higher than P(]0, 0.9]). So in this example, if I bought that security at the price whose logarithm is 1 (price = e^1) and I took profit if it reached the price whose logarithm is 1.1 (e^1.1) and closed with a loss if it reached e^0.9, I'd win in the long term.

I'm just a begginner in statistics, just started studying statistics this year. But I see many problems why this wouldn't work:

- First of all I don't know if prices really follow a log-normal distribution, I haven't found much information about this. I only know this is assumed in the black-scholes model, and that model is used to price options.

- The distribution function would change in time. As time passes, the mean would vary. Because of this I don't know if I can use this distribution that doesn't consider time.

If anyone knows statistics and probability theory here, what do you think?