Clearing price distributions in call auctions

M. Derksen, B. Kleijn and R. de Vilder

Quantitative Finance, 2020, vol. 20, issue 9, 1475-1493

Abstract: We propose a model for price formation in financial markets based on the clearing of a standard call auction with random orders, and verify its validity for prediction of the daily closing price distribution statistically. The model considers random buy and sell orders, placed employing demand- and supply-side valuation distributions; an equilibrium equation then leads to a distribution for clearing price and transacted volume. Bid and ask volumes are left as free parameters, permitting possibly heavy-tailed or very skewed order flow conditions. In highly liquid auctions, the clearing price distribution converges to an asymptotically normal central limit, with mean and variance in terms of supply/demand-valuation distributions and order flow imbalance. By means of simulations, we illustrate the influence of variations in order flow and valuation distributions on price/volume, noting a distinction between high- and low-volume auction price variance. To verify the validity of the model statistically, we predict a year's worth of daily closing price distributions for five constituents of the Eurostoxx 50 index; Kolmogorov–Smirnov statistics and QQ-plots demonstrate with ample statistical significance that the model predicts closing price distributions accurately, and compares favourably with alternative methods of prediction.

Date: 2020
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DOI: 10.1080/14697688.2020.1744699

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