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In most of the literature on the information content of various volatility estimator the relevant question is whether a particular estimator can predict (is correlated) with future realized volatility. Hence, the testing regression would be $$ RV(t,T) = \alpha + \beta VOL(t) + \epsilon(t) $$ where RV(t,T) is an estimate of the realized volatility from t to ...


Here it is: "Rebonato, R., Jackel, P. The most general methodology to create a valid correlation matrix for risk management and option pricing purposes." Recall: a covariance matrix will be the same as a correlation matrix if scale is removed. I used this method for ensuring positive definite correlations matrices.

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