Actual volatility, also known as future volatility, refers to the measurement of the fluctuation degree of investment income within the validity period of options. Because the return on investment is a random process, the actual volatility is always unknown. In other words, the actual volatility cannot be accurately calculated in advance, and people can only get its estimated value through various methods.
Historical volatility refers to the volatility of the return on investment in the past period, which is reflected by the historical data of the market price of the underlying assets in the past period (that is, the time series data of st). That is to say, according to the time series data of {St}, we can calculate the corresponding volatility data, and then estimate the standard deviation of the rate of return through statistical inference, so as to get the estimated value of historical volatility. Obviously, if the actual volatility is a constant and does not change with time, then the historical volatility may be a good approximation of the actual volatility.