Measures of Realized Variance

Intraday jump tests are shown to be sensitive to volatility patterns observed at different high frequencies of the data. The intraday variance shows a U shaped behavior. Volatility is high at the beginning of the trading day when the market opens and at the end of the day when the closing time approaches. The variance is low in between (and mainly around lunch time). A stream of literature has attempted to adjust volatility measures, both at the univariate and multivariate levels, in order to obtain a robust jump test statistic which is not dependent on the the volatility patterns and microstructure noise.

Two main periodicity estimation measures are proposed. The first is a classic estimate (Andersen and Bollerslev, 1997) and the second is robust to jumps (Boudt et al, 2011a).

Several volatility measures are then proposed to approximate the Integrated Volatility (IV). Some measures are suitable for an univariate setting and called robust to jumps i.e WSD (Boudt et al, 2011a), MinRV and MedRV (Andersen et al., 2012). Others can be used in an univariate or multivariate setting, i.e rBPCov (Barndorff-Nielsen et al., 2004), rOWCov (Boudt et al., 2011b). A third class of volatility measures is said to be robust to microstructure noise without necessarily being robust to jumps i.e rTSCov (Zhang, 2011), rAVGCov (Ait-Sahalia et al., 2005), rKernelCov (Barndorff-Nielsen et al., 2004). The only volatility measure robust to jump and microstructure noise jointly is the rRTSCov (Boudt and Zhang, 2013).

Correcting for periodicity while testing for intradaily jumps is of paramount importance since it may lead to type 1 and type 2 errors.

The graphs below plot the two periodicity estimates (Figure 1) and different volatility measures (Figure 2).

Figure 1: Periodicity in the 5 min EURUSD returns

Figure 1: Periodicity in the 5 min EURUSD returns

Figure 2: Realized Volatility Measures EURUSD

EURGBP

EURAUD

EURJPY

USDJPY

GBPUSD

SPX Index

CAC Index

UKX Index

DAX Index

NKY Index

HSI Index

The MinRv (Andersen et al, 2012) shows the lowest volatility for both exchange rates data and Stock market indices data while the rCov (Andersen et al., 2003) reveals the highest volatility level and seems to be more volatile than the MinRv, MedRv and rBPv. In addition, the rCov curve indicates several pics that correspond to the occurrence of jumps. The MedRv and rBPv (Realized Bipower Variation) lie between the MinRv and rCov with higher level of the the MedRv as compared to the rBPv.

 

References:

Ait-Sahalia, Y., Mykland, P. A., Zhang, L., (2005), A Tale of Two Time Scales: Determining Volatility With Noisy High-Frequency Data, Journal of American Statistical Association, 100, 1394-1411;

Andersen, T.,G., Bollerslev, T., (1997), Intraday Periodicity and Volatility Persistence in Financial Markets, Journal of Empirical Finance, 4, 115-158;

Boudt, K., Croux, C., Laurent, S., (2011a), Robust Estimation of Intraweek Periodicity in Volatility and Jump Detection, Journal of Empirical Finance, 18, 353-367;

Boudt, K, Croux, C, Laurent, S., (2011b), Outlying Weighted Covariation, Journal of Financial Econometrics, 9, 657-684;

Boudt, K., Zhang, J., (2013), Jump Robust Two Scale Covariance Estimation and Realized Volatility Budgets, Quantitative Finance, no. Published online: 18 Feb, 1-14;

Barndorff-Nielsen, O. E., Hansen, P. R., Lunde, A. and Shephard, N., (2004), Regular and Modified Kernel-Based Estimators of Integrated Variance: The Case With Independent Noise, Working paper;

Zhang, L., (2011), Estimating Covariation: Epps Effect, Microstructure Noise, Journal of Econometrics, 160, 33-47;