Random Walks, Market Efficiency, and Limit Order Book Models

Summary

The document raises a conceptual question about how quantitative and algorithmic trading firms can seek returns if asset prices follow random walks. It also asks whether random-walk behavior would undermine models of limit order books, using research that describes order-book dynamics through Markov processes and strategic interaction as an example.

The question points toward a useful distinction between unpredictable price changes and structured behavior in market mechanisms: order submissions, cancellations, and interactions may still be modeled even when price movements are difficult to forecast. However, the document contains no answers, evidence, or resolution of that distinction. It should be read as a prompt for further study rather than a conclusion about market efficiency, the profitability of quant strategies, or the predictive value of order-book models.

Key ideas

• The document asks how quantitative strategies can operate under random-walk descriptions of prices.
• It distinguishes the question of price predictability from the modeling of order-book activity.
• Markov-process models can represent evolving limit-order-book states and participant interactions.
• The text provides questions rather than evidence or answers about strategy performance or model usefulness.

Tags

# Random Walk Theory vs. Quant Trading


# Random Walk Theory vs. Quant Trading












I am quite new to random walk theory so please excuse my rather simply put question but I am wondering how can quant trading desks and other algorithmic trading firms exist if there is the random walk theory? Wouldn't it suggest if there is the random walk theory, noone can not outperform the market?

And as a second part of the question regarding random walks: Is there any research on random walks and the behaviour of limit order books? i.e. this Paper by Rosu models a limit-order book using Markov processes and a Markov perfect equilibirium: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=710841

Would a random walk in order book dynamics not suggest that models like this aren't of any use? To my understanding such a model makes sense, as there are agents interacting in a limit order-book that are to a substantial part algo trading driven and therefore they follow some kind of pattern that (should) make it possible to model this behaviour of such an limit order-book?

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