The realized power variations with even order of a discretely observed semi-martingale have been widely studied in literature, due to some important applications in finance, for example, estimating the integrated volatility and integrated quarticity. However, few works have paid attention to the...

The price staleness is referred to as the extent of the presence of the zero returns in the price dynamics. The proportion of the zero returns could be high in the high-frequency data sets, as pointed by Bandi et al. (2020a). Considering the price staleness as a dynamic system too, in this...

We provide theoretical and empirical justifications for linking the realised co-skewness between the VIX and the S&P 500 to conditional equity premiums. The realised co-skewness, as a measure of hedging benefits, shows a significant (and independent to that of the variance risk premium) negative...

The intraday high-frequency datasets contain several zero returns, which state that no change occurs in two or more consecutive transactions, particularly in the transaction data of in- active securities. In addition, existing approaches to cleaning financial data, such as the previous-tick...