Abstract
This paper develops methods and a framework of financial market theory. We model financial markets as a system of agents which perform market transactions with other agents under the action of numerous expectations. Agents’ expectations are formed of economic and financial variables, market transactions, the expectations of other agents, and other factors that impact financial markets. We use the risk ratings of agents as their coordinates and approximate a description of financial variables, market transactions, and expectations of numerous separate agents by density functions of aggregated agents in the economic domain. The motion of separate agents in the economic domain due to a change of agents’ risk rating produces collective financial flows of variables, transactions, and expectations. We derive equations on collective financial variables, market transactions, expectations, and their flows in the economic domain. These flows define the evolution of financial markets. As an example, we present a simple model with linear dependence between disturbances of volume and the cost of transactions on one hand, and disturbances of expectations that determine transactions on the other hand. Our model describes harmonique oscillations of these disturbances with numerous frequencies and allows an explicit form for fluctuations of price and return to be derived. These relations show a direct dependence between price, return, and volume perturbations.
Highlights
In recent decades, Econophysics has produced many studies for modeling financial markets and the statistical properties of price and return fluctuation: Mantegna and Stanley (2000), Gabaix et al (2003), Stanley (2003), and Borland and Bouchaud (2005)
Financial market and macro finance modeling heavily rely on methods of general equilibrium theory (GE) (Arrow and Debreu 1954; Arrow 1974; Kydland and Prescott 1990; Starr 2011) and DSGE (Fernández-Villaverde 2010; Komunjer and Ng 2011; Del Negro et al 2013; Farmer 2017)
We propose that fluctuations of macro variables, transactions, and expectations induced by oscillations of their flows and velocities due to borders of the economic domain (12c) and (12d) should be treated as business cycles
Summary
Econophysics has produced many studies for modeling financial markets and the statistical properties of price and return fluctuation: Mantegna and Stanley (2000), Gabaix et al (2003), Stanley (2003), and Borland and Bouchaud (2005). We develop methods, models, and equations, which treat financial variables, market transactions, and expectations as functions of risk. Agents’ expectations as drivers of transactions are responsible for financial activity and impact the evolution of macro variables Agents form their expectations as forecasts of variables, expectations of other agents, market regulatory trends, technology, climate, and other changes. We use risk ratings of agents as their coordinates; We describe variables, transactions and expectations as functions of risk; We describe collective flows of financial variables, transactions, and expectations and their impact on financial markets These issues will be discussed in detail
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