Price Distribution Systems
Price movement is usually seen as a chart in which each new time period is a new bar or point recorded to the right of the previous prices—the traditional time series. There are many applications that need to look at prices differently. In options, it is important to evaluate the current market volatility to decide the chances of prices remaining in a specific range for a specific amount of time. To get that value, we use the standard deviation calculation first introduced in Chapter 2. The standard deviation gives the most basic measure of price distribution. Although we apply the standard deviation to a time series, the daily price could be rearranged and the resulting standard deviation would still be the same. From the value of the standard deviation we can estimate the chances of a price remaining within a range over time. Because the standard deviation is the most commonly used measurement of price distribution, it is important to remember that a band formed by the average price change ±1 standard deviation contains 68% of the price movement (both up and down), ±2 standard deviations contain 95%, and ±3 standard deviations contain 99% of all price movement based entirely on the sample of data used to calculate the standard deviation value.
The data used to determine the standard deviation is very important. Because we are seeking a statistical measure, it is most accurate when a large amount of data is applied. ...