Probability Cone Pro

Probability Cone Pro is based on the Expected Move Pro. While Expected Move only shows the historical value band on every bar, probability cone extend the period in the future and plot a cone or curve shape of the probable range. It plots the range from bar 1 all the way to any specified number of bars up to 1000.



Probability Cone Pro is an upgraded version of the Probability Cone indicator that uses a Normal Distribution to model the returns. This newer version uses a maximum likelihood estimation for Asymmetric Laplace distribution parameters. Asymmetric Laplace distribution takes into account fatter tails and volatility clustering during low volatility. So it will be thinner in the body (eg: <70% range) and fatter in the tails (>95% range) which fits the stock return better. Despite a better fit users should not blindly follow the probabilities derived from the indicator and should understand that these are very precise estimations of probability based on historical data, not the true probability which is in reality unknown.



When we compare the more peaked asymmetric laplace to the bell curve shaped normal distribution we can see that the asymmetric laplace fits the empirical data (blue histogram) significantly better. The fit is improved in both the body (middle peaked part) as well as in the fatter tails (more of extreme occurrences far from the center)

The area of probability range is based on an inverse cumulative distribution function. The inverse cumulative distribution gives the range of price for given input probability. People can adjust the range by adjusting the input probability in the settings. The entered probability will be shown at the edges of the cone when the “show probability” setting is on.



The indicator allows for specifying the probability for 2 quantiles on each side of the distribution , therefore 4 distinct probability values. The exact probability input is another distinction compared to the Normal Distribution based Probability Cone, in which the probability range is determined by the input of a standard deviation. Additionally now the displayed labels at the edges of the probability cone no longer correspond to the total number of outcomes that are expected to occur within the specific range, instead we chose to display the inverse which is the probability of outcomes outside of the specified range. See comparison below:

Probability cone pro with 68% and 95% ranges also defined by 16% and 2.5% probabilities at the tails on both sides:

Normal Probability cone with 68% and 95% ranges defined by 1st and 2nd standard deviation


SETTINGS:

Bars Back: Number of bars the cone is offset by.
Forecast Bar: Number of bars we forecast the cone for in the future.
Lock Cone: Specify whether we wish t lock the cone to the current bar, so it does not move when new bars arrive.
Show Probability: Specify whether you wish to show the probability labels at the edges of the cone.
Source: Source for computation of log returns whose distribution we forecast
Drift: Whether to take into account the drift in returns or assume 0 mean for the distribution.
Period: The sampling period or lookback for both the drift and the volatility estimation (full distribution estimation).
Up/Down Probabilities: 4 distinct probabilities are specified, 2 for the upper and 2 for the lower side of the distribution.