Price, Volatility and the Second-Order Economic Theory

This paper considers price volatility as the reason for description of the second-degree economic variables, trades and expectations aggregated during certain time interval Δ. We call it - the second-order economic theory. The n-th degree products of costs and volumes of trades, performed by economic agents during interval Δ determine price n-th statistical moments. First two price statistical moments define volatility. To model volatility one needs description of the squares of trades aggregated during interval Δ. To describe price probability one needs all n-th statistical moments of price but that is almost impossible. We define squares of agent’s trades and macro expectations those approve the second-degree trades aggregated during interval Δ. We believe that agents perform trades under action of multiple expectations. We derive equations on the second-degree trades and expectations in economic space. As economic space we regard numerical continuous risk grades. Numerical risk grades are discussed at least for 80 years. We propose that econometrics permit accomplish risk assessment for almost all economic agents. Agents risk ratings distribute agents by economic space and define densities of macro second-degree trades and expectations. In the linear approximation we derive mean square price and volatility disturbances as functions of the first and second-degree trades disturbances. In simple approximation numerous expectations and their perturbations can cause small harmonic oscillations of the second-degree trades disturbances and induce harmonic oscillations of price and volatility perturbations.