Empirical estimation of realized higher-order (joint) cumulants and their practical issues

As conventional realized third and fourth (co)moments estimated with sub-period returns are biased, Neuberger (2012) and Bae and Lee (2021) develop new unbiased realized (joint) cumulants using extended information. In this paper, we discuss practical issues in estimating the realized (joint) cumulants. In addition, we estimate (joint) cumulants through various methods using simulated prices and examine the characteristics of those estimators. The simulation results show that realized (joint) cumulants estimated from sub-period returns and option data serve as proxies when the true realized cumulants are not obtainable. Lastly, we estimate realized (joint) cumulants using financial data on the S&P 500, individual stocks, and their options, and investigate whether the realized (joint) cumulants are explained by other estimators. As a result, we find that realized coskewness and kurtosis are predicted by implied moments and other lagged ex post estimators.