Five days of a hypothetical Nifty series:
| Day | Prev close | Open | High | Low | Close |
|---|---|---|---|---|---|
| 1 | 24,600 | 24,640 | 24,760 | 24,580 | 24,710 |
| 2 | 24,710 | 24,700 | 24,790 | 24,610 | 24,655 |
| 3 | 24,655 | 24,700 | 24,930 | 24,660 | 24,890 |
| 4 | 24,890 | 24,860 | 24,950 | 24,770 | 24,820 |
| 5 | 24,820 | 24,800 | 24,900 | 24,690 | 24,870 |
(a) Compute the annualised close-to-close volatility, once assuming zero mean () and once with the sample variance (ddof = 1). (b) Compute annualised Parkinson, Garman–Klass and Rogers–Satchell volatilities (mean of the per-day estimators). (c) Compute Yang–Zhang with . (d) Which number would you trust most for these five days, and why is the answer to (d) different from "the one with the highest efficiency"?