Historical Volatility is a measure of price fluctuation over time. Historical volatility uses historical (daily, weekly, monthly, quarterly, and yearly) price data to empirically measure the volatility of a market or instrument in the past. The value rendered by a historical volatility study is the standard deviation of bar-to-bar price differences. see, Sheldon Natenberg, Option Volatility and Pricing Strategies, Advanced Trading Techniques for Professionals, Chicago: Probus Publishing Company, 1988. [see Appendix B, The Mathematics of Option Pricing, p. 343 ff. for detailed information on standard deviation and historical volatility calculations]. Natenberg is an excellent source of information on using volatility studies to analyze options. On all historical charts, price differences are measured on a settlement-price to settlement-price basis. To calculate the historical volatility study, you must first identify the mean and then calculate the standard deviation: Formula: Standard Deviation, or Historical Volatility: Where: n = number of occurrences (bars) m = mean xi = price changes And: Mean: Where: m = mean n = number of occurrences xi = price changes And: xi can equal percent of price change: Or: xi can equal natural logarithmic price change: Historical Volatility
