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

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.

Bridging the Gap: Decoding the Intrinsic Nature of Time in Market Data

“…Within this new paradigm of intrinsic time, novel structures and regularities can be uncovered. For instance, a multitude of scaling laws emerges (Guillaume et al, 1997;Glattfelder et al, 2011), the concept of multi-scale liquidity is introduced (Golub et al, 2016), systematic trading strategies can be devised (Golub et al, 2018), a variation of the notion of volatility is defined (Petrov et al, 2019a), and an agent-based framework is formulated (Petrov et al, 2020). The notion of intrinsic time can be extended to a multi-dimensional methodology, incorporating more than one financial time series (Petrov et al, 2019b).…”

“…( 23) measure two distinct features of financial time series. The number of directional changes is a proxy for the volatility of the price process (Petrov et al, 2019a). Then, the overshoot lengths quantify the liquidity, where longer overshoots correspond to more illiquid markets (Golub et al, 2016).…”

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

“…Over the period T, the higher value of N DC indicates higher volatility. Petrov et al (2019) presented the measure of instantaneous volatility where the equation is developed based on the theory of Brownian motion for the price returns:…”

Computational Finance

“…Finally, using high-frequency data from several sources Petrov et al (2019) propose a novel intraday instantaneous volatility measure which utilises sequences of drawdowns and drawups as indicators of high-frequency activity of financial markets. The authors use their measure to uncover weekly seasonal patterns in volatility for three Forex and one Bitcoin exchange rates, as well as a stock market index.…”

“…The published papers develop new multivariate models, see Cheng et al (2019), considers option pricing in this challenging setting, see Reesor and Marshall (2020), and addresses issues related to risk management, see Cheng et al (2019), Forsyth andVetzal (2019), andVan Dijk et al (2018). The volume contains several papers that use simulation, see Dunne (2019), Létourneau and Stentoft (2019), Mukerji et al (2019), andStentoft (2019), and papers that provide new ways to model volatility, see Cheng et al (2019), and for estimating this, see Petrov et al (2019).…”