How Liquidity and Spreads Affect Hanson’s LMSR Market Maker

Summary

The note asks how Hanson’s logarithmic market scoring rule (LMSR) produces quoted outcome prices and whether trading pressure shifts prices in a see-saw pattern. The response says that this effect can be moderated by charging a wider spread, with the parameter b acting like a liquidity fund. Under the described interpretation, liquidity grows with trading volume and volatility decreases as volume accumulates.

The answer also claims that spreads can narrow as trading conveys information and contributes to liquidity, potentially making the market more efficient. It offers a qualitative explanation rather than a derivation of the quoted price formula or a worked market-making algorithm. It does not specify how to set the spread or parameter b, quantify the proposed effects, or discuss risks such as inventory exposure and adverse selection, so these claims should not be treated as a complete design or evaluation of an LMSR market maker.

Key ideas

• LMSR outcome prices respond to the relative quantities held across outcomes.
• The response describes a see-saw effect as trades shift quoted prices.
• A wider spread is proposed as a way to moderate volatility and contribute to liquidity.
• The explanation is qualitative and does not provide parameter-setting guidance or empirical evidence.
• A complete market-making design would require analysis beyond the effects described here.

Tags

# How does Hanson's Market Maker (LMSR) work?


# How does Hanson's Market Maker (LMSR) work?












Implementing Hanson's Market Maker states:

> If the market maker wants to quote a "current price", he can. The current price for outcome 1 is:

$$ \mbox{price1} = \frac{e^{\frac{q1}{b}}}{e^{\frac{q1}{b}} + e^{\frac{q2}{b}}} $$

Why this is the case? Is it just some simple "see-saw" algorithm? Exert pressure on one side and it will simply radiate across into the corresponding +/- price change?

I am asking in the context of writing a simple market-making algorithm to offer bids and quotes (on a virtual market), but this seems too simple.

## Answer by Ryan Singer (score 1)

https://quant.stackexchange.com/a/15542

It does create a see-saw. This can be reduced by having it charge a slightly bigger spread, which gets contributed to b. In this way, b effectively becomes a market making fund, and volatility decreases as trade volume increases. This makes the LMSR market maker liquidity sensitive.

This makes the market more efficient as spreads decrease over time as trading imparts price knowledge and subsidizes liquidity.

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