Comparative Analysis of Some Volatility Estimators: An Application to Historical Data from the Nigerian Stock Exchange Market

Abstract

Several models exist for estimating volatility of stocks. In this paper, comparisons are made for the performance characteristics of seven volatility estimators using the data for eleven Banks from the Nigerian Stock Exchange (NSE) daily prices for the period 3rd January 2006 to 31st December 2008. The estimations computed are: Standard Deviation, Historical Close-to-Close, Parkinson, Garman-Klass, Rogers-Satchell, Modified Garman-Klass and Yang Zhang volatility estimators. The volatility computations for the estimators employed the open, high, low and close values of daily prices using 5, 10 and 20 days intervals with no overlapping. The Models are automated using Microsoft Visual Basic Express Edition with the volatilities output generated by the estimators further analysed using SPSS and Microsoft Excel software packages. The criteria used to evaluate the performances of these volatility estimators are the Mean Absolute Deviation (MAD), Standard Error (STDERR) and Efficiency. The Efficiency test compares the relative uncertainty of the various estimators using standard deviation as the benchmark while the MAD and STDERR are used to find the mean absolute deviation and the standard error of the estimators respectively. In terms of MAD and STDERR, the Parkinson model performs better than other estimators while the Garman-Klass performs better than other estimators in Efficiency. The only common finding is that the Standard Deviation estimator is the least performing of the estimators. Finally, the levels of correlation between volatility estimators are found to be very high.