A practical model for prediction of intraday volatility

Although intraday volatility has been studied extensively for many asset classes, there are still important questions to be answered: Is the unconditional mean diurnal profile time-invariant? Does statistical ergodicity hold for the profile? Is it possible to predict intraday volatility in absolute terms? In this study, we explore answers to these questions. Intraday bar data are collected for securities in Russell 3000 Index, FTSE 100 Index and CAC All-Tradable Index. For intraday volatility measure, we choose the one that makes use of open-high-low-close prices of each time bucket. We first propose a predictive model where the intraday volatility is decomposed into three multiplicative components: daily volatility, time-scaling factor, and normalized diurnal profile. We then estimate unconditional mean diurnal profiles of securities in four market capitalization groups: MEGA-, BIG-, MID-, and SMALL-CAP over time and observe that they are time invariant. We further compare time-averaged with ensemble-averaged diurnal profiles and find that strict statistical ergodicity doesn’t hold but the two are not far apart. Finally we evaluate model performance using both timeseries and cross-sectional approaches and conclude that both approaches are unbiased.

Data

Daily and intraday market price data for securities in three equity indices: Russell 3000 Index, FTSE 100 Index, and CAC All-Tradable Index.

Decomposition of intraday volatility

In this study, we choose to use a published intraday volatility measure involving open-high-low-close prices. It’s shown to be more efficient than the conventional one using only close prices. This measure is calculated for each intraday time interval, forming a diurnal profile.

We build our intraday volatility prediction model by decomposing it into three multiplicative components: daily volatility estimate, the ratio between average intraday volatility level and daily volatility, and an intraday periodic component. The ratio is introduced to account for the effect of time scaling of volatility: it can be considered a factor of conversion from daily volatility to intraday volatility mean level.

Daily volatility prediction using EWMA

We use the exponentially weighted moving average model (EWMA) for prediction of daily volatility. The decay factor recommended in Risk Metrics for daily timeseries is used. This prediction serves as the driving force of intraday volatility.

Intraday volatility profile estimation

We use two approaches to estimate the time-scaling factor and diurnal profile:

• timeseries-based: the time-scaling factor and diurnal profile are estimated as averages over time for the same security,
• cross-section or ensemble-based: the time-scaling factor and diurnal profile are estimated as averages over securities in an ensemble. The market capitalization group is treated as the ensemble in this study. Four capitalization groups are defined: MEGA-, BIG-, MID-, and SMALL-CAP.

Main results

• The periodic diurnal profile is approximately time-invariant,
• securities traded in London and Paris exchanges demonstrate a significant intraday volatility jump attributed to the opening of US stock markets,
• the time- and ensemble-averaged diurnal profiles do not overlap, indicating that statistical ergodicity doesn’t hold strictly; but the two are not far apart,
• both timeseries- and cross-section-based predictors are unbiased.

Download the whitepaper to learn more about profiling and prediction of intraday volatility.