1,808 research outputs found
Most Efficient Homogeneous Volatility Estimators
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.Comment: 46 pages including 17 figure
Spurious trend switching phenomena in financial markets
The observations of power laws in the time to extrema of volatility, volume and intertrade times, from milliseconds to years reported by Preis et al. (2010, 2011), are shown to result straightforwardly from the selection of biased statistical subsets of realizations in otherwise featureless processes such as random walks. The bias stems from the selection of price peaks that imposes a condition on the statistics of price change and of trade volumes that skew their distributions. For the intertrade times, the extrema and power laws results from the format of transaction dat
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