Estymacja wariancji arytmetycznego ruchu Browna na podstawie znanych wartości minimum, maksimum, końcowej oraz dryfu
Estimation of Arithmetic Brownian Motion Variance when Values of Minimum, Maximum, Finish and Drift are Known

Summary/Abstract: This paper examines the problem of calculating the variance of returns of a financial instrument which is based upon the historical opening, closing, high, and low prices. For this purpose the joint distribution of minimum, maximum and final values of arithmetic Brownian motion was used. It gave a possibility to make a comparative analysis of the variance estimators. The formulae of expected values of many random variables, which were used for the construction of these estimators were calculated. Moreover, on the basis of those formulae, the new estimator of variance was proposed. The assumptions that were adopted for the construction of the estimator were examined. The efficiency of the proposed estimator was compared with the efficiency of the well-known estimators of daily volatility.

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