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Jun 17

A Comparative Study of Range-based Stock Return Volatility Estimators for the German Market

Posted by abiao at 14:05 | Paper Review | Comments(0) | Reads(9032)
Needless to say, volatility estimation is crucial for finance application, chasing for a more accurate volatility estimate method seems endless and is always at the center of finance research. In the paper A Comparative Study of Range-based Stock Return Volatility Estimators for the German Market by Neda Todorova, Sven Husmann, the authors investigate the relative performance of various volatility estimators based on daily and intraday price ranges of 25 German equities, using the two scales realized volatility of Zhang, Mykland, and Ait-Sahalia (2005) as a benchmark.

Generally, range-based estimators assume that the price process follows a geometric Brownian motion, the authors start from two upward biased volatility estimates with zero-drift assumption. (O, C, H, and L denote the log of the opening, closing, highest, and lowest price, respectively)
Parkinson (1980)
Parkinson
Garman and Klass (1980)
Garman and Klass
Rogers and Satchell (1991) develops a more efficient estimator without zero-drift assumption afterwards
Rogers and Satchell

All three estimators above are calculated assuming that stock trading is continuous, however, it is not in practice and discrete trading is therefore expected to cause a downward bias. To get rid of the bias, correction procedures are developed
Adjusted Rogers and Satchell
adjusted Rogers and Satchell
Adjusted Garman and Klass
adjusted Garman and Klass

So far the above mentioned estimators use daily data only, with the availability of intraday data and hence more information captured, Martens and van Dijk (2007) and Christensen and Podolskij (2007) combine the concepts of range based and realized volatility. Specifically, define a typical realized range as
realized range
Martens and van Dijk (2007) propose a scaling bias-correction realized range
Martens and van Dijk
Instead of the scaling factor 0.3607, Christensen and Podolskij (2007) suggest another factor
Christensen and Podolskij
with lambda being the second moment of a standard Brownian motion over a unit interval and can be simulated.

Finally the authors compare all of those estimators using 25 German stocks and the two scales realized volatility of Zhang, Mykland, and Ait-Sahalia (2005) as a benchmark, they show that all estimators based on daily ranges are by far superior to the classical estimator, the realized range obtained from intraday ranges performs better in terms of both bias and efficiency, in addition, the bias correcting procedure developed by Christensen and Podolskij (2007) consistently outperform all other alternatives.

PS: all of the equations are from the paper A Comparative Study of Range-based Stock Return Volatility Estimators for the German Market by Neda Todorova, Sven Husmann downloadable at http://onlinelibrary.wiley.com/doi/10.1002/fut.20534/pdf. You can find matlab codes on historical volatility estimation shared earlier.


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