Bootstrapping Realized Volatility in the presence of Intra-day Periodicity


  • Jorren Jacobs



When looking at prices in the stock market, it becomes clear that these prices are rather volatile. This means that prices vary over the day. Estimating the degree of variation through the day is of great importance to practitioners in the financial markets, and has therefore become a popular topic in financial econometric literature. The more prices are observed throughout the day the more accurately one can estimate the daily volatility. However, as is the problem with any estimation, we cannot say with 100% certainty that the estimated value is equal to the true value. What we can do is construct a confidence interval around our estimate. A confidence interval states that the true value lies within a specified range with a certain probability. In order to do this we need two things: we need to know the variance of our estimator and we need to know its distribution. Although the first issue can be dealt with, the second issue proves itself to be difficult. The goal of my bachelor thesis was to investigate the effect of assuming an intra-day periodicity factor in the volatility of the stock price on the ability of the bootstrap methods to provide better confidence intervals.


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

Andersen, T. G., & Bollerslev, T. (1998). Answering the Skeptics: Yes, Standard Volatility Models do Provide Accurate Forecasts. International Economic Review, 39, 885-905.

Andersen, T. G., & Bollerslev, T. (1998). DM-Dollar volatility: intraday activity patterns, macroeconomic announcements and longer run dependencies. The Journal of Finance, 53, 219-265,

Andersen, T. G., Bollerslev, T., Diebold, F., & Labys, P. (2001). The Distribution of Realized Exchange Rate Volatility. Journal of the American Statistical Association, 96, 42-55.

Barndor-Nielsen, O., & Shephard, N. (2001). Non-Gaussian Ornstein-Uhlenbeck-Based Models and Some of Their Uses in Financial Economics, (with discussion) Journal of the Royal Statistical Society, Series B, 63, 167-241.

Barndor-Nielsen, O., & Shephard, N. (2002). Econometric analysis of realized volatility and its use in estimating stochastic volatility models, Journal of the Royal Statistical Society, Series B, 64, 253-280.

Boudt, K., Croux, C., & Laurent, S. (2008). Robust estimation of intraweek periodicity in volatility and jump detection. Mimeo.

Goncalves, S., & Meddahi, N. (2009). Bootstrapping Realized Volatility, Econometrica, 77(1), 283-306.

Hecq, A., Laurent, S., & Palm, F. (2012). Common Intraday Periodicity. Journal of Financial Econometrics, Oxford University Press, 10(2), 325-353.

Jacod, J. (1994). Limit of random measures associated with the increments of a Brownian semimartingale, Preprint number 120, Laboratoire de Probabilitit_es, Universit_e Pierre et Marie Curie, Paris.

Jacod, J., & Protter, P. (1998). Asymptotic error distributions for the Euler method for stochastic differential equations. Annals of Probability 26, 267-307.

Taylor, S., & Xu, X. (1997). The incremental volatility information in one million foreign exchange quotations. Journal of Empirical Finance, 4, 317-340.