In this publication Vladimir Petrov (University of Zurich), Anton Golub (Flov technologies), Richard Olsen (Lykke) uncover weekly instantaneous volatility seasonality patterns of Bitcoin prices and compare it to the seasonality of three Forex exchange rates.
New instantaneous volatility measure based on the analysis of alternating price trends is proposed. The measure is agnostic to the flow of physical time and is equally applicable to all high-frequency tick-by-tick prices. Alternating drawdowns and drawups have been adapted to perform as indicators of the market’s activity. The authors re-expressed these quantities in terms of directional-change intrinsic time.
This concept dissects a price curve into a collection of consecutive positive and negative returns measured from local extremes. Interdependence of the instantaneous volatility and the number of directional changes was employed to discover the seasonality patterns. Analytical expressions connecting the waiting times and the number of directional changes have been validated by Monte Carlo simulation. Time intervals throughout which the statistical weekly volatility activity is constant were applied to demonstrate the long memory of the number of directional changes and instantaneous volatility. Provided volatility estimation method can be adapted as a universal multiscale risk-management tool not restricted by the continuity of physical time.