Power law in tails of bourse volatility – evidence from India
-
Author(s)Bikramaditya GhoshLink to ORCID Index: https://orcid.org/0000-0003-0686-7046
,
M. C. KrishnaLink to ORCID Index: https://orcid.org/0000-0002-4060-8550
-
DOIhttp://dx.doi.org/10.21511/imfi.16(1).2019.23
-
Article InfoVolume 16 2019, Issue #1, pp. 291-298
- Cited by
- 1023 Views
-
151 Downloads
This work is licensed under a
Creative Commons Attribution 4.0 International License
Inverse cubic law has been an established Econophysics law. However, it has been only carried out on the distribution tails of the log returns of different asset classes (stocks, commodities, etc.). Financial Reynolds number, an Econophysics proxy for bourse volatility has been tested here with Hill estimator to find similar outcome. The Tail exponent or α ≈ 3, is found to be well outside the Levy regime (0 < α < 2). This confirms that asymptotic decay pattern for the cumulative distribution in fat tails following inverse cubic law. Hence, volatility like stock returns also follow inverse cubic law, thus stay way outside the Levy regime. This piece of work finds the volatility proxy (econophysical) to be following asymptotic decay with tail exponent or α ≈ 3, or, in simple terms, ‘inverse cubic law’. Risk (volatility proxy) and return (log returns) being two inseparable components of quantitative finance have been found to follow the similar law as well. Hence, inverse cubic law truly becomes universal in quantitative finance.
- Keywords
-
JEL Classification (Paper profile tab)B23, B41, C18
-
References37
-
Tables1
-
Figures0
-
- Table 1. Comparison of the power law exponent of the cumulative distribution function for various index based volatility proxy (financial Reynolds number)
-
- Abhyankar, A., Copeland, L. S., & Wong, W. (1995). Moment Condition Failure in High Frequency Financial Data: Evidence from the S&P 500. Applied Economics Letters, 2(8), 288-290.
- Arms, Richard W. (1996). Trading without Fear (1st ed.). John Wiley and Sons.
- Bachelier, L. (1900). Th’eorie de La Sp’ Eculation. Annales scientifiques de l’École Normale Supérieure, 17, 21-86.
- Botta, F., Moat, H. S., Stanley, H. E., & Preis, T. (2015). Quantifying Stock Return Distributions in Financial Markets. PLoS ONE, 10(9), 1-10.
- Bree, D. S., & Joseph, N. L. (2013). Fitting the Log Periodic Power Law to Financial Crashes: A Critical Analysis. ArXiv:1002.1010v2, 1-30.
- Ding, Z., Granger, C. W. J., & Engle, R. F. (1993). A Long Memory Property of Stock Returns and a New Model. Journal of Empirical Finance, 1(1), 83-106.
- Dorsey, D. (1993). Technical Analysis of Stocks and Commodities. New York.
- Fama, E. F. (1965). The Behavior of Stock-Market Prices. The Journal of Business, 38(1), 34-105.
- Farmer, D., & Geanakoplos, J. (2011). Power Laws in Economics and Finance. SSRN Electronic Journal, 1-57.
- Fisher, R. A., & Tippett, L. H. C. (1928). Limiting Forms of the Fre Quency Distribution of the Largest or Smallest Member of a Sample. Proceedings of the Cambridge Philosophical Society, 24(2), 180-290.
- Gabaix, X. (2016). Power Laws in Economics: An Introduction. Journal of Economic Perspective, 30(1), 185-206.
- Gardes, L., & Girard, S. (2008). A Moving Window Approach for Nonparametric Estimation of the Conditional Tail Index. Journal of Multivariate Analysis, 99(10), 2368-2388.
- Gardes, L., & Girard, S. (2010). Conditional Extremes from Heavy-Tailed Distributions: An Application to the Estimation of Extreme Rainfall Return Levels. Extremes, 13(2), 177-204.
- Garman, M. B., & Klass, M. J. (1980). On the Estimation of Security Price Volatilities from Historical Data. Journal of Business, 53(1), 67-78.
- Gibrat, R. (1931). Les Inégalités Économiques; Ap- Plications: Aux Inégalités Des Richesses, à La Con- Centration Des Entreprises, Aux Populations Des Villes, Aux Statistiques Des Familles, Etc., d’une Loi Nouvelle, La Loi de l’effet Proportionnel. Libraire Du Recueil Sirey. Paris.
- Hill, B. (1975). A Simple General Approach to Inference about the Tail of a Distribution. The Annals of Statistics, 3(5), 1163-1174.
- Jansen, D. W., & De Vries, C. G. (1991). On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective. The Review of Economics and Statistics, 73(1), 18-24.
- Kelly, B. (2014). The Dynamic Power Law Model. Extremes, 17(4), 557-583.
- Kyle, A., & Obizhaeva, A. (2013). Large Bets and Stock Market Crashes (AFA 2013 San Diego Meetings Paper).
- Kyle, A., & Obizhaeva, A. (2016). Market Microstructure Invariance: Empirical Hypotheses. Econometrica, 84(4), 1345-1404.
- Laloux, L., Potters, M., Cont, R., Aguilar, J. P., & Bouchaud, J. P. (1998). Are Financial Crashes Predictable? Europhysics Letters, 45, 1-5.
- Loretan, M., & Philips, P. (1994). Testing the Covariance Stationarity of Heavy-Tailed Time Series: An Overview of the Theory with Applications to Several Financial Datasets. Journal of Empirical Finance, 1(2), 211-248.
- Lux, T. (1996). The Stable Paretian Hypothesis and the Frequency of Large Returns. Applied Financial Economics, 6, 463-475.
- Mandelbrot, B. B. (1963). The Variation of Certain Speculative Prices. In Fractals and Scaling in Finance. Journal of Business, 36(4), 394-419.
- Mantegna, R. N., & Stanley, H. E. (1995). Scaling Behaviour in the Dynamics of an Economic Index. Nature, 376, 46-49.
- Nirei, M., Stachurski, J., Takaoka, K., & Watanabe, T. (2018). Herding and Power Laws in Financial Markets Herding and Power Laws in Financial Markets (CARF-F-434, F-434).
- Pan, R. K., & Sinha, S. (2008). Inverse-Cubic Law of Index Fluctuation Distribution in Indian Markets. Physica A: Statistical Mechanics and Its Applications, 387(8-9), 2055-2065.
- Pape, B. (2007). Asset Allocation and Multivariate Position Based Trading. Journal of Economic Interaction and Coordination, 2(2), 163-193.
- Parkinson, M. (1980). The Extreme Value Method for Estimating the Variance of the Rate of Return. Journal of Business, 53(1), 61-65.
- Plerou, V., Gopikrishnan, P., Gabaix, X., & Stanley, H. E. (2004). On the Origin of Power-Law Fluctuations in Stock Prices. Quantitative Finance, 11-15.
- Reynolds, O. (1883). An Experimental Investigation of the Circumstances Which Determine Whether the Motion of Water Shall Be Direct or Sinuous, and of the Law of Resistance in Parallel Channels. Proceedings of the Royal Society of London, 84-99.
- Reynolds, O. (1901). Papers on Mechanical and Physical Subjects. Reprinted from Various Transactions and Journals, 2, 1881-1900.
- Rosen, S. (1981). The Economics of Superstars. The American Economic Review, 71(5), 845-858.
- Sornette, D. (2003). Why Stock Markets Crash, Critical Events in Complex Financial Systems. Princeton University Press.
- Velasco, C., & Lobato, I. N. (2000). Long-Memory in Stock-Market Trading Volume. Journal of Business & Economic Statistics, 18(4), 410-427.
- Wiggins, J. B. (1992). Estimating the Volatility of S&P 500 Futures Prices Using the Extreme Value Method. Journal of Futures Markets, 12, 265-273.
- Wu, L. (2006). Dampened Power Law: Reconciling the Tail Behavior of Financial Security Returns. Journal of Business, 79(3), 1445-1473.
-
Identifying explosive behavioral trace in the CNX Nifty Index: a quantum finance approach
Bikramaditya Ghosh ,
Emira Kozarević
doi: http://dx.doi.org/10.21511/imfi.15(1).2018.18
Investment Management and Financial Innovations Volume 15, 2018 Issue #1 pp. 208-223 Views: 2233 Downloads: 5435 TO CITE АНОТАЦІЯThe financial markets are found to be finite Hilbert space, inside which the stocks are displaying their wave-particle duality. The Reynolds number, an age old fluid mechanics theory, has been redefined in investment finance domain to identify possible explosive moments in the stock exchange. CNX Nifty Index, a known index on the National Stock Exchange of India Ltd., has been put to the test under this situation. The Reynolds number (its financial version) has been predicted, as well as connected with plausible behavioral rationale. While predicting, both econometric and machine-learning approaches have been put into use. The primary objective of this paper is to set up an efficient econophysics’ proxy for stock exchange explosion. The secondary objective of the paper is to predict the Reynolds number for the future. Last but not least, this paper aims to trace back the behavioral links as well.
-
Predictability and herding of bourse volatility: an econophysics analogue
Bikramaditya Ghosh ,
Krishna M.C. ,
Shrikanth Rao ,
Emira Kozarević ,
Rahul Kumar Pandey
doi: http://dx.doi.org/10.21511/imfi.15(2).2018.28
Investment Management and Financial Innovations Volume 15, 2018 Issue #2 pp. 317-326 Views: 2078 Downloads: 218 TO CITE АНОТАЦІЯFinancial Reynolds number works as a proxy for volatility in stock markets. This piece of work helps to identify the predictability and herd behavior embedded in the financial Reynolds number (time series) series for both CNX Nifty Regular and CNX Nifty High Frequency Trading domains. Hurst exponent and fractal dimension have been used to carry out this work. Results confirm conclusive evidence of predictability and herd behavior for both the indices. However, it has been observed that CNX Nifty High Frequency Trading domain (represented by its corresponding financial Reynolds number) is more predictable and has traces of significant herd behavior. The pattern of the predictability has been found to follow a quadratic equation.
-
Multifractal analysis of volatility for detection of herding and bubble: evidence from CNX Nifty HFT
Bikramaditya Ghosh ,
Emira Kozarević
doi: http://dx.doi.org/10.21511/imfi.16(3).2019.17
Investment Management and Financial Innovations Volume 16, 2019 Issue #3 pp. 182-193 Views: 1012 Downloads: 310 TO CITE АНОТАЦІЯThis study delves into the herding and bubble detection in the volatility domain of a capital market underlying. Furthermore, it focuses on creating heuristics, so that common investors find it relatively easy to understand the state of the market volatility. Hence, it can be termed that this study is focused on the specific financial innovation regarding bubble and herding detection coupled with investor awareness. The traces of possible volatility bubble emerge when it is positioned against its own lags (both lag1 and lag2). The volatility trigger indicated clear traces of herding and an embedded parabola function. Continuous and repetitive parabola function hinted at a subtle presence of “fractals”. Firstly, the detrended fluctuation analysis has been used with its multifractal variant. Secondly, the regularized form of Hurst calculation and analysis have been used. Both tests reveal the traces of nascent bubble formation owing to prominent herding in CNX Nifty HFT environment. They also indicate a clear link with Hausdorff topological patterns. These patterns would help to create heuristics, enabling investors to be aware of possible bubble and herd situations.
