Price, Volatility and the Second-Order Economic Theory

This paper models price volatility through description of the second-degree transactions and expectations averaged by time interval Δ. We call it - the second-order economic theory. 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 should model all n-th price statistical moments but that seems almost implausible. Hence the desire to find out the price probability will remain unfeasible. We assume that it is possible to accomplish risk assessment for almost all economic agents. Agents risk ratings distribute agents, their transactions and expectations in economic space determined by numerical continuous risk grades. We define aggregate squares of agents transactions and introduce expectations those approve the second-degree transactions executed during interval Δ. We derive equations on the second-degree transactions and expectations in economic space. 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