Distribution of price and volume in a call auction

Martin ŠmÍd and AleŠ AntonÌn KubĚna

Quantitative Finance, 2026, vol. 26, issue 4, 525-540

Abstract: We study a call auction model with general demand and supply curves. Buy and sell orders arrive randomly and, on average, generate these curves. The model generalizes several existing models. While only conditional distributions of the clearing price and traded volume have been mathematically described in the literature, we derive both the exact and asymptotic unconditional distributions of these quantities. We demonstrate the rapid convergence of the asymptotic distributions to the exact ones. The model is able to reproduce fat-tailed behaviour of the clearing price. In particular, we show that the quotes (bid and ask) inherit the tail behaviour of the demand and/or supply curves, and that fat tails in the price distribution may alternatively be caused by order imbalance.

Date: 2026
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DOI: 10.1080/14697688.2026.2636565

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