Modeling Call Auction Clearing Prices from Random Order Flow

Summary

This study models price formation in a standard call auction by treating buy and sell orders as random draws from valuation distributions. An equilibrium condition yields distributions for both the clearing price and traded volume. Bid and ask volumes remain flexible parameters, allowing the model to represent skewed or heavy-tailed order flow. Under high liquidity, the clearing price approaches a normal distribution whose mean and variance depend on valuations and order-flow imbalance.

Simulations examine how changes in valuations and order flow affect prices, volumes, and price variance across high- and low-volume auctions. For empirical evaluation, the authors forecast daily closing price distributions for five Eurostoxx 50 constituents over a year. Kolmogorov-Smirnov statistics and QQ plots support the model’s fit and show favorable comparisons with alternative forecasting methods. The reported evidence is limited to those stocks and the stated period; the excerpt does not establish performance in other markets or auction settings.

Key ideas

• Random buy and sell orders are modeled using separate demand and supply valuation distributions.
• An equilibrium condition produces distributions for auction clearing price and traded volume.
• The model permits flexible bid and ask volumes to represent imbalanced or heavy-tailed flow.
• With high liquidity, clearing prices approach a normal distribution.
• Tests on five Eurostoxx 50 stocks use distributional diagnostics and comparisons with other methods.

Tags

# Clearing price distributions in call auctions


# Clearing price distributions in call auctions









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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