Power law in tails of bourse volatility – evidence from India


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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.

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    • Table 1. Comparison of the power law exponent of the cumulative distribution function for various index based volatility proxy (financial Reynolds number)