I stumbled upon a problem of converting the returns and volatility of high frequency data to daily ones. I start with 1-minute returns, then calculate the 5-minute realized variance as the sum of the squared log returns over the 5 minute window. I also calculate the realized covariance with the benchmark. Ultimately, I want to calculate the 5-min volatility and beta using 1-minute data.
However, I am using a variety of products. Some of them are traded at NYSE, where trading takes place over 6,5h a day, some in London (8,5 hours of trading) and the indices are quoted 24/7. So my question is how I can bring all these measures to one frequency (daily)?