Implications of market microstructure for realized variance measurement

Volatility measuring and estimation based on intra-day high-frequency data has grown in popularity during the last few years. A significant part of the research uses volatility and variance measures based on the sum of squared high-frequency returns. These volatility measures, introduced and mathematically justified in a series of papers by Andersen et al. [1999. (Understanding, optimizing, using and forecasting) realized volatility and correlation. Leonard N. Stern School Finance Department Working Paper Series, 99-061, NewYork University; 2000a. The distribution of realized exchange rate volatility. Journal of the American Statistical Association 96, no. 453: 42-55; 2000b. Exchange rate returns standardized by realized volatility are (nearly) Gaussian. Multinational Finance Journal 4, no. 3/4: 159-179; 2003. Modeling and forecasting realized volatility. NBER Working Paper Series 8160.] and Andersen et al. [2001a. Modeling and forecasting realized volatility. NBER Working Paper Series 8160.], are referred to as 'realized variance'. From the theory of quadratic variations of diffusions, it is possible to show that realized variance measures, based on sufficiently frequently sampled returns, are error-free volatility estimates. Our objective here is to examine realized variance measures, where well-documented market microstructure effects, such as return autocorrelation and volatility clustering, are included in the return generating process. Our findings are that the use of squared returns as a measure for realized variance will lead to estimation errors on sampling frequencies adopted in the literature. In the case of return autocorrelation, there will be systematic biases. Further, we establish increased standard deviation in the error between measured and real variance as sampling frequency decreases and when volatility is non-constant.