The Market-Based Asset Price Probability

We consider the time-series records of the market trade values and volumes as the origin of the asset price stochasticity and describe random price properties through statistical moments of the market trade values and volumes. The market-based price probability differs from the conventional price probability proportional to number of trades at price p. We show that the market-based price probability results no correlations between n-th degrees of price and trade volume but doesn’t cause statistical independence of price and trade volume. We derive the market-based correlation between price and squares of the trade volumes. Time-series records of the market trade values and volumes allow assess only finite number m of statistical moments and define first m price statistical moments. Approximations of the price characteristic function that match first m price statistical moments generate approximations of the market-based price probability. That approach unifies description of the asset price, returns, inflation and their volatilities as functions of the market trade values and volumes statistical moments. That describes the case when investor’s market trades impact asset price probability. Market-based approach uncovers vital fault of the Value-at-Risk (VaR) as most conventional hedging tool. We show that accuracy of VaR assessment at horizon T is determined by precision of predictions of the market trade values and volumes statistical moments and depends on accuracy of macroeconomic forecasting. The market-based approach to price probability establishes direct economic ties between the asset pricing, market stochasticity and economic theory.