The impact of trading volume on the stock market credibility: Bohmian quantum potential approach

Price return is an interesting factor for many investors; however, it is expected that the price return to be affected by the trading volume of any given market as a complex system. The Bohmian quantum mechanics is used due to the time correlation of return and volume of the stock markets under consideration. Recent studies have shown that the quantum potential given by the Bohmian quantum mechanics confines price return variations into a definite interval. In this study, we extend the quantum potential concept to investigate the behavior of trading volume and its possible influences on the price return. The obtained results show that the quantum potential behaves in the same manner for trading volume as the price return, and confines the variations of the volume into a specific domain. Furthermore, a joint quantum potential as a function of return and volume is derived by the probability distribution function (PDF) constructed by the real data of a given market. It serves as a suitable instrument to investigate the relationship between these variables and to check the credibility of the market at higher volumes. The resultant PDF and the corresponding joint quantum potential illustrate that the variations of price return at higher volumes decrease as the trading volume increases, making the market more credible which is more pronounced in developed markets.