Bikramaditya Ghosh

The 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.

Financial 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.

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.

This 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.

Long-range dependence (LRD) in financial markets remains a key factor in determining whether there is market memory, herding traces, or a bubble in the economy. Usually referred to as ‘Long Memory’, LRD has remained a key parameter even today since the mid-1970s. In November 2016, a sudden and drastic demonetization measure took place in the Indian market, aimed at curbing money laundering and terrorist funding. This study is an attempt to identify market behavior using long-range dependence during those few days in demonetization. Besides, it tries to identify nascent traces of bubble and embedded herding during that time. Auto Regressive Fractionally Integrated Moving Average (ARFIMA) is used for three consecutive days around the event. Tick-by-tick data from CNX Nifty High Frequency Trading (CNX Nifty HFT) is used for three consecutive days around demonetization (approximately, 5000 data points from morning trading sessions on each of the three days). The results show a clear and profound presence of herd behavior in all three data sets. The herd intensity remained similar, indicating a unique mixture of both ‘Noah Effect’ and ‘Joseph Effect’, proving a clear regime switch. However, the results on the event day show stable and prominent herding. Mandelbrot’s specified effects were tested on an uncertain and sudden financial event in India and proved to function perfectly.

EURIBOR emerged as a conventional proxy for a risk-free rate for a reasonably long period of time after the creation of the Eurozone. However, the joy was short-lived, as the global credit crisis shook the markets in mid-2008. Significant counterparty risk embedded in a derivative transaction cannot be left out. EURIBOR reflects the credit spread on borrowing. Hence, risk and uncertainty are inextricably linked here. This study investigates five banks out of 19 panel banks that manage EURIBOR in various Eurozone countries. These banks, HSBC, ING, Deutsche Bank, the National Bank of Greece and Barclays, are tested from January 2009 to December 2017 on a daily basis. Bank specific EURIBOR can be predicted in all five cases with different degrees. The trace of a profound herd is observed in the case of the National Bank of Greece, others were relatively mild in nature. The customer base and their risk grade were recognized as the main factor. Their information asymmetry and derived information entropy suggest embedded chaos and uncertainty.