Volatility Depend on Market Trades and Macro Theory

This paper presents probability distributions for price and returns random processes for averaging time interval Δ. These probabilities determine properties of price and returns volatility. We define statistical moments for price and returns random processes as functions of the costs and the volumes of market trades aggregated during interval Δ. These sets of statistical moments determine characteristic functionals for price and returns probability distributions. Volatilities are described by first two statistical moments. Second statistical moments are described by functions of second degree of the cost and the volumes of market trades aggregated during interval Δ. We present price and returns volatilities as functions of number of trades and second degree costs and volumes of market trades aggregated during interval Δ. These expressions support numerous results on correlations between returns volatility, number of trades and the volume of market transactions. Forecasting the price and returns volatilities depend on modeling the second degree of the costs and the volumes of market trades aggregated during interval Δ. Second degree market trades impact second degree of macro variables and expectations. Description of the second degree market trades, macro variables and expectations doubles the complexity of the current macroeconomic and financial theory.