# Clearing price distributions in call auctions

## TL;DR

This paper introduces a model for price formation in call auctions that predicts daily closing price distributions using demand and supply valuations, validated with Eurostoxx 50 data.

## Contribution

It develops a novel equilibrium-based model for call auction prices that accounts for heavy-tailed and skewed order flows, validated with real market data.

## Key findings

- Model accurately predicts daily closing price distributions.
- In highly liquid auctions, prices tend to a normal distribution.
- Order flow variations significantly influence price and volume distributions.

## Abstract

We propose a model for price formation in financial markets based on 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 following 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 5 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.

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Source: https://tomesphere.com/paper/1904.07583