*Article* **Instantaneous Volatility Seasonality of High-Frequency Markets in Directional-Change Intrinsic Time**

### **Vladimir Petrov 1,\*,†, Anton Golub 2 and Richard Olsen 3**


Received: 28 February 2019; Accepted: 26 March 2019; Published: 1 April 2019

**Abstract:** We propose a novel intraday instantaneous volatility measure which utilises sequences of drawdowns and drawups non-equidistantly spaced in physical time as indicators of high-frequency activity of financial markets. The sequences are re-expressed in terms of directional-change intrinsic time which ticks only when the price curve changes the direction of its trend by a given relative value. We employ the proposed measure to uncover weekly volatility seasonality patterns of three Forex and one Bitcoin exchange rates, as well as a stock market index. We demonstrate the long memory of instantaneous volatility computed in directional-change intrinsic time. The provided volatility estimation method can be adapted as a universal multiscale risk-management tool independent of the discreteness and the type of analysed high-frequency data.

**Keywords:** instantaneous volatility; directional-change; seasonality; forex; bitcoin; S&P500; risk management; drawdown
