24-Hour realized volatilities and transatlantic volatility interdependence

Abstract

This paper proposes an innovative econometric approach for the computation of 24-h realized volatilities across stock markets in Europe and the US. In particular, we deal with the problem of non-synchronous trading hours and intermittent high-frequency data during overnight non-trading periods. Using high-frequency data for the Euro Stoxx 50 and the S&P 500 Index between 2003 and 2011, we combine squared overnight returns and realized daytime variances to obtain synchronous 24-h realized volatilities for both markets. Specifically, we use a piece-wise weighting procedure for daytime and overnight information to take into account structural breaks in the relation between the two. To demonstrate the new possibilities that our approach opens up, we use the new 24-h volatilities to estimate a bivariate extension of Corsi et al.’s [Econom. Rev., 2008, 27(1–3), 46–78] HAR-GARCH model. The results suggest that the contemporaneous transatlantic volatility interdependence is remarkably stable over the sample period.

Keywords:

• High-frequency data
• Realized volatility
• HAR-GARCH
• Volatility interdependence

JEL Classifications:

• C58
• G15

Acknowledgements

We thank Robert Jung, Asger Lunde and Massimiliano Caporin for valuable comments and suggestions. Further, we thank the participants of the 14th IWH-CIREQ Macroeconometric Workshop on Forecasting and Big Data, the participants of the Joint Doctoral Seminar in Econometrics of the University of Hohenheim and Tübingen, the participants of the 2nd CIdE Workshop in Econometrics and Empirical Economics as well as the participants of the Swedish Central Bank’s research seminar. Moreover, we gratefully acknowledge financial support from the Fritz Thyssen Foundation.

Notes

No potential conflict of interest was reported by the author.

1 In case of non-synchronous returns and positive correlation, the true correlation is underestimated. For extensive documentations of this problem, see Martens and Poon (2001) or Schotman and Zalewska (2006).

2 Note that we focus on the realized volatility, whereas Hansen and Lunde (2005) actually focus on realized variances. However, the realized variance and the realized volatility are closely related. The latter can be obtained from extracting the square root of the realized variance. In the following, we use RV to denote the realized volatility and RVAR to denote the realized variance.

3 So far, the literature has been confined to the analysis of short time periods. Hansen and Lunde (2005), for example, consider a sample from January 2001 to December 2004, whereas Masuda and Morimoto (2012) use a sample from January 2004 to November 2006.

4 One hour has to be subtracted from the winter trading times to obtain the trading times in summer. Note that we also take non-synchronous time-shifts in Europe and the US into account.

5 Note that these times were given throughout the whole sample period, apart from a short exception at the beginning of the sample period. From 2 June 2000 onwards, trading hours in Europe were extended until 19:00 UTC. However, as the trading volume was only small over this period, the extended trading hours were disestablished on 31 October 2003. We do not consider extended hours trading in October 2003.

6 On the one hand, a bias might arise from market microstructure noise, for example, due to non-synchronous trading. On the other hand, the volatility rises as a consequence of discretization if the frequency is lowered.

7 Note that stale information is contained in index opening prices, if not all stocks are traded immediately at the beginning of a trading day. As nowadays most stocks tend to be traded very shortly after market opening, however, the economic implications of this problem become negligible after very short time (see e.g. Jung and Maderitsch 2014).

8 More precisely, we discard 9 days from our 1964 days sample (the 5 days with the highest realized variances over the active trading periods and the 4 days with the highest overnight returns). Hansen and Lunde (2005) exclude 10 days in total from their 986 days total sample.

9 However, different stochastic processes are possible. E.g. a relatively higher weekend variance is allowed as long as it is proportional to .

10 Note that we consider these regressions only as crude checks of the assumptions. We use them due to a lack of alternatives, being well aware of the fact that classical time series regression assumptions might not be fully met in these potentially dynamically incomplete regressions.

11 Note that proceeding this way appeared most straightforward to us to test the stability of the linear regression relations presented in Hansen and Lunde (2005). However, there might be other methods, for example, based on economic theory, that might lead to meaningful subsamples as well.

12 The graphical results for the F-statistics are depicted in figure B1 in the appendix. The boundaries are computed such that the probability that the supremum F-statistic exceeds them is .

13 Short-term volatility, for example, might be unimportant for investors with long-term trading horizons, but not vice versa.

14 Note, however, that after taking collinearity between the realized volatility components into account by estimating a model with orthogonalized volatility components according to Souček and Todorova (2013), we find the dependence on the daily volatility component to increase and the dependence on the monthly component to decrease. All other coefficients remain virtually unchanged.

15 Note that under , the constant conditional correlation (CCC) model according to Bollerslev (1990) is nested in the varying conditional correlation model.

16 Note that in this context, we also test the auxiliary V-HAR model for the presence of structural breaks in linear regression relations over time. At least for the US market, we find evidence for breaks at the beginning of the financial crisis of 2007 and the European sovereign debt crisis since 2008. Taking these breaks into account and re-estimating both time-varying and constant conditional correlation models, however, leaves the main results virtually unchanged. As the auxiliary model is not of central interest to us, we find it well justifiable to present the time-varying conditional correlations over the total sample period.

18 Hence: .

19 Note, however, that even if our realized volatility estimator was biased, then this would only be problematic if the bias was not proportional to . Experimenting with volatility signature plots, however, we do not find evidence for the presence of considerable market microstructure noise.

20 Detailed results are available upon request.