Price Discovery In Financial Markets: Analysis Of Two Systems Of Differential Equations

We present two systems of differential equations implied by two different models of price discovery. One is the basic Walrasian model, where prices adjust to a security’s own excess demand. The basic Walrasian model does not feature cross-security effects (the price of one security reacts to excess demand in another). The alternative is a model where demand adjusts autonomously to perceived excess demand, and prices adjust as the result of changes in the marginal valuation at the new demand. The alternative model explains why there would be cross-security effects. If there are cross-security effects, stability (convergence) is far from a foregone conclusion, but the cross-security effects implied by the autonomous-demand price discovery model ensures global stability. When adding a simple gaussian shock in the form of increments of a Brownian motion, the resulting stochastic versions of the price discovery models never imply excess kurtosis. Experimental data strongly support the main conclusion of both models, that price changes are correlated with excess demand. Also, once episodes of little or no price movements (price changes less than or equal to one tick) are eliminated, prices in the experiments do not exhibit excess kurtosis. The significant cross-security effects in experimental data leads us to reject the basic Walrasian model. The alternative model essentially captures the cross-security effects, implying that demand in the experimental markets largely changes autonomously, and price changes are only derivative.