Volatility Models: Historical volatility (HV)
Volatility, determined on a basis of the past price levels. Two numbers are necessary for calculation of HV. The first - what value of the
price we take on the current bar - for example: close, (high+low)/2, (open+high+low+close)/4 and so on. The second number is the range
of a time window. It is not clear how long should be the time of sampling. However, it is common to use the past 20 or 60 days period.
Classical estimator: it requires only closing prices  and can be defined as the
standard deviation  of the daily price returns for a period of time 
 (2.1)
This is the optimal (maximum likelihood) estimator obtained from random walk model.
Parkinson (1980): this estimator uses extreme value, the highs  and the lows
 during the day.
(2.2)
This is five times more efficient than the close-to-close estimate. (That means, for the same amount of data the variance of the data is
one fifth that of the close-to-close measure.)
Garman & Klass (1980): this estimator 7.4 times more efficient than close to close
(2.3)
Rogers & Satchell (1991): Rogers & Satchel estimator is independent of the drift
(2.4)
HV is rather easy to count up and interpret for stationary time series. Unfortunately, the financial time series are not stationary.
Future volatility (FV)
Future volatility is AV over period to expiry of the option. In the Black-Scholes world some average value of FV defines the option price.
FV is a key notion because it is a measure of uncertainty about future price movements, because it is directly related to the risk
associated with holding financial se-curities.
Unknown.
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