Volatility Depend on Market Trades and Macro Theory

Abstract

We show that the price and returns volatilities depend on the first and the second degree of the total values and the total volumes of the transactions aggregated during averaging time interval Δ. We derive expressions that describe price volatility via volatilities of the value and the volume and the number of trades during interval Δ. We introduce notions of the value and the volume returns and describe price returns volatility through volatilities of the volume and the value returns and number of trades during Δ. We describe price and returns random processes probability distributions by the complete set of statistical moments determined by corresponding n-th degrees products of the values and the volumes of the executed market transactions. Adequate model of volatility requires macroeconomic theory that describes second-degree value and volume of transactions, the second-degree macro variables and expectations. This problem doubles the complexity of the current macroeconomic and financial theory.

Keywords: price and returns volatility, price-volume relations, macro theory

JEL Classification: D4, E3, E44, G1, G2