Price, Volatility and the Second-Order Economic Theory

Abstract

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.

Theoretical Economics and the Second-Order Economic Theory. What is it?

“…We propose move to numerical continuous risk grades and develop distributions of economic agents by their risk grades. Theory, based on distributions of economic agents by their risk grades gives a powerful tool for description of agent's variables, trades and expectations (Olkhov, 2016(Olkhov, -2021a. Business cycles and price fluctuations, economic waves and option pricing can be described via unified theoretical approach.…”

“…These expectations can be created by state and forecasts of the first order variables and by second order variables and by other factors as well. As we show in (Olkhov, 2021a), assessment of average expectations should be made by weighting expectations by the value and volume of trades, made under these expectations. If so, the most influential expectations of the first order trades can be different from most influential expectations of the second order trades.…”

“…That is the next level of complexity of economic theory that complement conventional macroeconomic modeling. The first step in the development of second order economic theory is presented in (Olkhov, 2021a).…”

Three Remarks On Asset Pricing

“…Forecasts of kurtosis require the forth-order economic theory and so on. For brevity we don't consider here the problems of description of the second-order economic theory and refer for details to (Olkhov, 2020b).…”

To VaR, or Not to VaR, That is the Question

“…Why do they have economic sense and why (3.2; 3.5) don't use the frequency trade data to introduce the price probability distribution? Our respond is simple and clearrelations (3.2; 3. diversified portfolios requires modeling wide range of macroeconomic and macro financial variables and transactions those impact market trends, investment priorities, prospect inflation and etc… Moreover, as we discussed in (Olkhov, 2020b), current economic models describe relations between macroeconomic and financial variables and transactions of the first order. Macroeconomic investment, demand, consumption, trade volumes and etc., are formed as sum of the first order investment, consumption and trade of economic agents that can be presented as relations of the volume U(1;t) and the value C(1;t) of the first degree.…”