  To take into account the temporal dimension of uncertainty in stock markets,
this paper introduces a cross-sectional estimation of stock market volatility
based on the intrinsic entropy model. The proposed cross-sectional intrinsic
entropy (CSIE) is defined and computed as a daily volatility estimate for the
entire market, grounded on the daily traded prices: open, high, low, and close
prices (OHLC), along with the daily traded volume for all symbols listed on The
New York Stock Exchange (NYSE) and The National Association of Securities
Dealers Automated Quotations (NASDAQ). We perform a comparative analysis
between the time series obtained from the CSIE and the historical volatility as
provided by the estimators: close-to-close, Parkinson, Garman-Klass,
Rogers-Satchell, Yang-Zhang, and intrinsic entropy (IE), defined and computed
from historical OHLC daily prices of the Standard & Poor's 500 index (S&P500),
Dow Jones Industrial Average (DJIA), and the NASDAQ Composite index,
respectively, for various time intervals. Our study uses approximately 6000 day
reference points, starting on 1 Jan. 2001, until 23 Jan. 2022, for both the
NYSE and the NASDAQ. We found that the CSIE market volatility estimator is
consistently at least 10 times more sensitive to market changes, compared to
the volatility estimate captured through the market indices. Furthermore, beta
values confirm a consistently lower volatility risk for market indices overall,
between 50% and 90% lower, compared to the volatility risk of the entire market
in various time intervals and rolling windows.
