Measuring relative volatility in high-frequency data under the directional change approach

We introduce a new approach in measuring relative volatility between two markets based on the directional change (DC) method. DC is a data-driven approach for sampling financial market data such that the data are recorded when the price changes have reached a significant amplitude rather than recording data under a predetermined timescale. Under the DC framework, we propose a new concept of DC micro-market relative volatility to evaluate relative volatility between two markets. Unlike the time-series method, micro-market relative volatility redefines the time-scale based on the frequency of the observed DC data between the two markets. We show that it is useful for measuring the relative volatility in micro-market activities (high-frequency data).