good questions... ding..

这个标准差公式只是一个最普通的算法，波动率还有很多其他算法，可以包含开盘价，日内最高最低等等，可以参考Volatility Trading by Euan Sinclair(论坛里有这书）。日内高频数据的已实现波动率也有不一样的算法，相关论文也不少。你得到的数据应该不会是一天1440分钟都有吧，如果是股票一共才交易4个小时。

1. Theoretically use trading hours*60. The reason is the same as how you calc the annualized daily volatility. Remember in step 2. when you calc std, you actually average the squared return by 252. So the number of period to calc std should be consistentw with the number of period you put in the square. But intraday data is more noisy, you'd better need other ways to model and calc it.

2. because you divide 252 in calc std, you already assumed the 252 business days return are i.i.d, which means they have no autocorrelation, no weekend effect. But what you said makes some sense, because the return from Friday to Monday usually contains more info.Then what you can do is either omit it or multiply 1/3 of that F-M return. Or do a regression to see on average how much that return is higher in magnitude than normal weekdays' return.

3. Theoretically it should be. But it also depends the data period you are choosing.

首先，谢谢Chemist_MZ的热心解答，

1、关于问题1，先抛开噪音的问题不考虑，那您的应该是 std*sqrt(252 * 4 * 60)？感觉这样应该更合理点。

2、这点您说的对，计算时其实已经默认为收益独立不相关了，我貌似看过有些结论说是实际的F-M波动比平时的波动大概高20%~30%左右，小于理论上日期的差别带来的波动差别。

3、关于这点还是不太理解，我当时计算取的是相同时期，
比如分钟数据为：p_1_1，...，p_1_240，p_2_1，...，p_2_240，...，p_n_1，...，p_n_240，
按这些1分钟数据计算得到1个年化波动率std1，
然后再取每天最后一个数据，也即：p_1_240，p_2_240，...，p_n_240，也计算出一个波动率std2
这里算出的std1<std2
和感觉上不太一样，逻辑上有什么说法可以解释么？

非常感谢，我去查查看您说的资料。