Continuous Prices, Order Book Competition, and Trading Costs

Summary

The document considers a hypothetical market in which stock prices can vary continuously, asking whether traders would keep improving the best bid and offer until a trade occurs. The response points out that real order books operate through discrete events, making the premise difficult to apply directly to actual markets. It offers no model, data, or empirical test of a truly continuous-price market.

As an economic intuition, it suggests that transaction costs and adverse selection can make further quote improvement unprofitable, limiting the incentive to undercut or outbid existing orders. If quotes do converge until the spread vanishes, incoming bid and ask orders could match. These are qualitative possibilities rather than a complete account of order priority, market design, or trader behavior, so the discussion should be treated as a brief thought experiment.

Key ideas

• Real order books update through discrete events, so a continuously varying price is a hypothetical premise.
• Transaction costs and adverse selection may discourage traders from continually improving their quotes.
• If the best bid and ask converge, orders on opposite sides may match.
• The explanation is qualitative and does not model a specific market mechanism.

Tags

# continuous stock price


# continuous stock price












I wonder what would happen if the stock price becomes continuous? I am thinking that if that happens, everyone just places a limit bid order just above the original best bid order or limit sell order below the original sell order. Will there be a trade?

## Answer by ltrd (score 3)

https://quant.stackexchange.com/a/44207

It is rather philosophical or fantasy question because most of the orderbooks are event-driven, so they are discrete from definition. Honestly, I cannot even imagine how this could be a problem in a continuous time.

However, due to transaction costs, adverse selection and other problem realted to the High Frequency Trading, probably there wouldn't be problems describing by you, because from some point placing new best bid or ask order would be unprofitable. Of course it would also be a situation where new best bid and new best ask order would be matched due to spread equals 1 tick.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.