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, the historic and implied volatilities are compared to decide the chances of prices remaining in a specific range for a specific amount of time. When a risk manager evaluates the volatility of performance, the same annualized standard deviation calculation is used. This was introduced in Chapter 2. The standard deviation gives the most basic and accepted measure of price distribution. From 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 99.7% of all price movement. Theoretically, all price movement should be contained within the range of ±3.5 standard deviations.
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. For example, the annualized volatility (using daily returns) of crude oil from 1983 ...