This Demonstration calculates the probability that the random price of the exchange-traded fund, SPY, will be higher or lower after one month than a particular future possibility.

Stable distributions are controlled by four parameters,

,

,

,

. When the shape parameter

, the distribution is normal; when

, the distribution has infinite variance; and when

, the distribution has no mean. The other parameters are

, the skewness parameter;

, the scale parameter; and

, the location parameter, which is the mean of the distribution when

.

The calculation uses a stable distribution model, with parameters

,

,

,

derived from intraday data from the last mid 2007 to December 2008.

The calculation is based on the last price, which you must set first either with the slider or by directly entering the price. You can then move the future price slider to calculate the probabilities along the curve for various future prices.