To calculate volatility, which price in FTSE table is used? When do we use close price for calculating volatility? Do we use adjclose (adjusted close price) for calculating volatility as well? when and how do we use adjclose price?
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The adjusted close price accounts for corporate actions such as stock splits and dividends, distributions and rights offerings (here)
Stock splits in particular would give the illusion of significant volatility and impact your estimates with outliers that are not due to market activity. Therefore, I would suggest using the adjusted close prices.
That said, and depending of what exactly you are trying to achieve, you may still need to treat cash dividends and rights offerings with special care.