  We present a comprehensive theory of homogeneous volatility (and variance)
estimators of arbitrary stochastic processes that fully exploit the OHLC (open,
high, low, close) prices. For this, we develop the theory of most efficient
point-wise homogeneous OHLC volatility estimators, valid for any price
processes. We introduce the "quasi-unbiased estimators", that can address any
type of desirable constraints. The main tool of our theory is the parsimonious
encoding of all the information contained in the OHLC prices for a given time
interval in the form of the joint distributions of the high-minus-open,
low-minus-open and close-minus-open values, whose analytical expression is
derived exactly for Wiener processes with drift. The distributions can be
calculated to yield the most efficient estimators associated with any
statistical properties of the underlying log-price stochastic process. Applied
to Wiener processes for log-prices with drift, we provide explicit analytical
expressions for the most efficient point-wise volatility and variance
estimators, based on the analytical expression of the joint distribution of the
high-minus-open, low-minus-open and close-minus-open values. The efficiency of
the new proposed estimators is favorably compared with that of the
Garman-Klass, Roger-Satchell and maximum likelihood estimators.
