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Calculated probabilities ploted on a risk graphGo To Options Analysis Software

  
 

Statistics - Option Pricing

  
 

A normal distribution curve (sometimes called as the bell curve because the graph of its probability density resembles a bell) describes the likely outcome of random events. To put it as simply as possible: if you track a stock for one year, it means that this statistical test has 252 cites (trading days) and every day you write down the rate of change from the last day.

  
  Bell curve, normal distribution  
 

In normal distribution, almost all values lie within three standard deviations of the mean.

1. About 68% of the values lie within one standard deviation of the mean (or between the mean minus 1 times the standard deviation, and the mean plus 1 times the standard deviation).

2. About 95% of the values lie within two standard deviations from the mean (or between the mean minus 2 times the standard deviation, and the mean plus 2 times the standard deviation). 

3. Almost all (actually, 99.7%) of the values lie within 3 standard deviations from the mean (or between the mean minus 3 times the standard deviation and the mean plus 3 times the standard deviation).

This rule is used to quickly get a rough estimate of something's probability, given its standard deviation.

For example, there is about a 68% probability that the stock will trade in a range of 12% (from +6% to -6%), about one standard deviation from the mean to each side and 27% probability (95% - 68% = 27%) that the stock will trade over 6% or below -6%, two standard deviations from the mean. We can also say that the stocks probability to range from -10% to +10% is about 95%.  

  
  Volatility graphs: The tallest graph shows the lowest volatility, while the lowest graph shows the highest volatility.  
 

Volatility graphs: The tallest graph shows the lowest volatility, while the lowest graph shows the highest volatility. Let's say if the taller graph volatility is 10%, the volatile financial instrument will be about 15% and a high-volatility financial instrument will be about 20%. Because volatility and implied volatility are worth detailed coverage, the next article is an elaboration of the terminology and reveals ways to exploit this knowledge to your benefit.