Markets: A Rigorous Course

M09 · Problem 1 ★ Check

Realised volatility from OHLC

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 (1n∑rt2\frac1n\sum r_t^2) 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 n=5n=5. (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"?

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Commas, ₹, % and 1e-3 notation are accepted.

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