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We study the price dynamics of 65 stocks from the Dow Jones Composite Average from 1973 until 2014. We show that it is possible to define a Daily Market Volatility $sigma(t)$ which is directly observable from data. This quantity is usually indirectly defined by $r(t)=sigma(t) omega(t)$ where the $r(t)$ are the daily returns of the market index and the $omega(t)$ are i.i.d. random variables with vanishing average and unitary variance. The relation $r(t)=sigma(t) omega(t)$ alone is unable to give an operative definition of the index volatility, which remains unobservable. On the contrary, we show that using the whole information available in the market, the index volatility can be operatively defined and detected.
We investigate scaling and memory effects in return intervals between price volatilities above a certain threshold $q$ for the Japanese stock market using daily and intraday data sets. We find that the distribution of return intervals can be approxim
This paper presents probability distributions for price and returns random processes for averaging time interval {Delta}. These probabilities determine properties of price and returns volatility. We define statistical moments for price and returns ra
One of the major issues studied in finance that has always intrigued, both scholars and practitioners, and to which no unified theory has yet been discovered, is the reason why prices move over time. Since there are several well-known traditional tec
Econophysics and econometrics agree that there is a correlation between volume and volatility in a time series. Using empirical data and their distributions, we further investigate this correlation and discover new ways that volatility and volume int
In informationally efficient financial markets, option prices and this implied volatility should immediately be adjusted to new information that arrives along with a jump in underlyings return, whereas gradual changes in implied volatility would indi