This paper introduces alternative measurements that use additional information of prices during the day: opening, minimum, maximum, and closing prices. Using the binomial model as the distribution of the stock price we prove that these alternative measurements are more efficient than the traditional ones that rely only in closing price. Following Garman and Klass (1980) we compute the relative efficiency of these measurements showing that are 3 to 4 times more efficient than using closing prices. Using daily data of the Chilean stock market index we show that a discrete-time approximation of the stock price seems to be more accurate than the continuous-time model. Also, we prove that there is a high correlation between intraday volatility measurements and implied ones obtained from options market (VIX). For that we propose the use of intraday information to estimate volatility for the cases where the stock markets do not have an associated option market.
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