The econophysics of asset prices, returns and multiple expectations

Victor Olkhov

Abstract

We model interactions between financial transactions and expectations and describe asset pricing and return disturbances. We use the risk ratings of economic agents as their coordinates, and we approximate the financial variables, transactions and expectations of numerous separate agents by descriptions of collective variables, transactions and expectations as density functions in the economic space. We take into account flows of collective financial variables, transactions and expectations induced by the motion of separate agents in the economic space due to the change of agents' risk ratings and describe the impact of these flows. We derive self-consistent equations on transactions and multiple kinds of expectations and propose that asset pricing fluctuations may be induced by different expectations for approved transactions with particular assets. We study a model with a linear dependence between the disturbances of transactions and expectations and derive expressions that describe the explicit dependence between price and volume disturbances and the dependence between return and volume disturbances. Our results may help in further studies of price–volume and return–volume correlations.