Pricing Stocks with Trading Volumes (CSIAM Transactions on Applied Mathematics, 2024)
The present paper proposes a new framework for describing the stock pricedynamics. In the traditional geometric Brownian motion model and its variants, volatility plays a vital role. The modern studies of asset pricing expand around volatility,trying to improve the understanding of it and remove the gap between the theoryand market data. Unlike this, we propose to replace volatility with trading volumein stock pricing models. This pricing strategy is based on two hypotheses: A price-volume relation with an idea borrowed from fluid flows and a white-noise hypothesisfor the price rate of change (ROC) that is verified via statistic testing on actual marketdata. The new framework can be easily adopted to local volume and stochastic volumemodels for the option pricing problem, which will point out a new possible directionfor this central problem in quantitative finance.