# Optimal auction duration: A price formation viewpoint

## TL;DR

This paper analyzes how the duration of auctions affects price accuracy, deriving an optimal time frame that balances volume and price efficiency, and compares it to continuous trading systems.

## Contribution

It introduces a semi-explicit formula for auction price error based on duration and market behavior, and identifies optimal auction durations for real stocks.

## Key findings

- Optimal auction durations range from 2 to 10 minutes.
- Continuous limit order books are generally sub-optimal for price formation.
- Market behavior significantly influences auction price accuracy.

## Abstract

We consider an auction market in which market makers fill the order book during a given time period while some other investors send market orders. We define the clearing price of the auction as the price maximizing the exchanged volume at the clearing time according to the supply and demand of each market participants. Then we derive in a semi-explicit form the error made between this clearing price and the efficient price as a function of the auction duration. We study the impact of the behavior of market takers on this error. To do so we consider the case of naive market takers and that of rational market takers playing a Nash equilibrium to minimize their transaction costs. We compute the optimal duration of the auctions for 77 stocks traded on Euronext and compare the quality of price formation process under this optimal value to the case of a continuous limit order book. Continuous limit order books are found to be usually sub-optimal. However, in term of our metric, they only moderately impair the quality of price formation process. Order of magnitude of optimal auction durations is from 2 to 10 minutes.