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 timescale 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).