Modeling and Analysis of Trading Volume and Stock Return Data Using Bivariate q-Gaussian Distribution

Two known characteristics of the distribution of stock returns (price fluctuations) and, more recently, the distribution of financial asset volumes are power laws and scaling. These power laws can be viewed as the asymptotic behaviour of distributions derived from nonextensive statistics, as demonstrated by an extensive number of instances in the field of physics. In this study, we explain the application of a non-extended statistics-based model for trading volume and stock price data. We present some novel theoretical results for the correlation between the trading volume distribution and stock return volatility that comes from entropy optimisation. We named this probability distribution as a bivariate q-Gaussian distribution since the resulting distribution is in terms of the q-exponential function, and when q tends to 1, it goes to the bivariate normal distribution. The primary characteristics of the novel model are thoroughly examined. The maximum likelihood estimation, a conventional technique, is used to conduct parameter estimation. The utility of the framing model is demonstrated using BSE Sensex data, which is used to illustrate the application of the bivariate q-Gaussian distribution.