The following table presents sample daily historical price data for a stock whose returns are given in the third column.

a. Based on a traditional sample estimator, calculate a daily variance estimator for this stock.

b. Assume that returns follow a Brownian motion process (at least that stock returns are uncorrelated over time) and that there are 30 trading days per month. What would be the monthly variance for this stock?

c. What would be the Parkinson extreme value estimated daily returns variance for this stock?

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Time 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Pricet Returnt 30.000 N.A. 30.125 30.250 30.125 32.000 34.000 0.00417 0.00415 -0.00413 0.06224 0.06250 31.000 -0.08824 32.000 0.03226 30.500 -0.04688 30.750 30.875 31.000 0.00820 0.00407 0.00405 30.875 -0.00403 31.000 0.00405 31.125 0.00403 30.250 -0.02811 33.000 0.09091 30.000 -0.09091 35.125 0.17083 33.000 -0.06050 32.125 -0.02652 32.250 0.00389 32.375 0.00388 32.125 -0.00772 32.250 0.00389 34.250 0.06202 36.375 0.06204 38.500 0.05842 34.375 -0.10714 33.875 -0.01455 33.625 -0.00738