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This paper investigates the return-volatility asymmetry of Bitcoin. We find that the cross correlations between return and volatility (squared return) are mostly insignificant on a daily level. In the high-frequency region, we find thata power-law appears in negative cross correlation between returns and future volatilities, which suggests that the cross correlation is revision{long ranged}. We also calculate a cross correlation between returns and the power of absolute returns, and we find that the strength of revision{the cross correlations} depends on the value of the power.
We study the volatility time series of 1137 most traded stocks in the US stock markets for the two-year period 2001-02 and analyze their return intervals $tau$, which are time intervals between volatilities above a given threshold $q$. We explore the
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
The distribution of the return intervals $tau$ between volatilities above a threshold $q$ for financial records has been approximated by a scaling behavior. To explore how accurate is the scaling and therefore understand the underlined non-linear mec
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
Bid-ask spread is taken as an important measure of the financial market liquidity. In this article, we study the dynamics of the spread return and the spread volatility of four liquid stocks in the Chinese stock market, including the memory effect an