Information Theoretic Ranking of Extreme Value Returns


This study highlights the importance of the information contained extreme value ratios (or returns) in the volatility estimation of financial assets. Most popular extreme value estimators like Parkinson (Journal of Business, 61–65, 1980), Garman Klass (Journal of business, 67–78, 1980), Rogers Satchell (The Annals of Applied Probability, 504–512, 1991) and Yang Zhang (The Journal of Business, 73 (3), 477–492, 2000) use a subset of all available extreme value ratios but not the full set. We examine if there are other extreme value ratios which contain more information than the most widely used ratios. This study shows empirically how much information is contained in various extreme value ratios of financial assets, using both real and simulated data. Using information theory, we find out their variability in relation to a uniform distribution in each quarter. We then rank them using the Kullback–Leibler metric (in accordance with a scoring methodology we developed in this study) to ascertain which set of ratios are more variable than others and thus may provide better estimation in computing volatility. We also calculate the rank of the matrix to identify the set of linearly independent ratios, for ascertaining the number of ratios that would be enough to generate a class of volatility estimators. The empirical results demonstrate that the need for incorporating other ratios in volatility estimation. We also observe that each dataset has other more informative ratios which are uniquely attributed to that dataset.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.


  1. 1.

    We could not include the ranking scores of all the ratios due to brevity. However it can be made available on request.


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Corresponding author

Correspondence to Parthajit Kayal.



Appendix A: Score Tables for Real Data

See appendix Tables 12, 13, 14, 15, 16.

Table 12 Scores for Crude Oil Simple Ratios
Table 13 Scores for 20 most informative Crude Oil derived ratios
Table 14 Scores for Gold Futures Simple Ratios
Table 15 Scores for 20 most informative Gold Futures derived ratios
Table 16 Scores for Crude Oil Simple Ratios

Appendix B: Score Tables for Simulated Data

See appendix Tables 16, 17, 18, 19.

Table 17 Scores for 20 most informative Crude Oil derived ratios
Table 18 Scores for Gold Futures Simple Ratios
Table 19 Scores for 20 most informative Gold Futures derived ratios

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Kayal, P., Dutta, S., Khandelwal, V. et al. Information Theoretic Ranking of Extreme Value Returns. J. Quant. Econ. 19, 1–21 (2021).

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  • Extreme value estimators
  • Information theory
  • Volatility

JEL Classification

  • G10
  • G140
  • G150
  • G170