Market Impact Models and Estimating Price Response to Order Flow

Summary

The document asks how to model the relationship between signed trading volume and price changes, using a simplified Kyle-style expression in which price impact is proportional to signed volume. It also asks whether least squares is appropriate for estimating such a linear relationship from observations. The answer offers only a short pointer to several theoretical papers on trading, information, and price formation; it does not explain their models or provide empirical comparisons.

As a result, the material is best treated as an entry point to market microstructure research rather than a practical modeling guide. It provides no dataset, fitted coefficients, diagnostics, or evidence that a linear impact function is suitable across real markets. Applying the suggested regression would require careful definitions of order flow and price changes, along with attention to timing, confounding information, market conditions, and statistical dependence. Those issues are not addressed in the document, so it cannot establish which model fits best or how well the proposed form performs.

Key ideas

• The document frames market impact as a possible relationship between signed volume and price changes.
• A Kyle-style specification represents price changes as proportional to signed order flow.
• Least squares is raised as a possible way to estimate a linear relationship, but no procedure is developed.
• The answer points to theoretical literature without summarizing its models or empirical findings.
• The document does not establish that a linear impact model fits real markets well.

Tags

# Relation between price changes and trading volume (market impact)


# Relation between price changes and trading volume (market impact)












It is quite a well-know phenomenon that trading volume has an impact on a stock price: the more you buy the higher is a price because of demand increment. I'm wondering about models that can describe it formally. So I have two questions.

- What are the best models that fit it? For example, I know about Kyle's model (link) that says that $p_T = p_0 + \sum\limits_{n=0}^{N-1}\Delta p_n = p_0 + \lambda\sum\limits_{n=0}^{N-1}\varepsilon_n v_n$, where $p_T$ and $p_0$ are prices at $t=T$ and $t=0$ correspondingly, $\varepsilon_n=1$ if the volume of buys $v_b$ is larger than the volume of sells $v_s$ in the time interval $\Delta t$, $\varepsilon_n=-1$ in the opposite case and $v=\vert v_b - v_s\vert$. Is it suitable for real markets or does there exist something better?

- What statistical methods are usually used when you want to create some model from data or test some model for fitting the data? I think if we are seeking for linear dependence (as Kyle model told) between price and volume then least squares method will be fine for plotting a line between discrete data points.

Any thoughts and suggestions will be very appreciative.

## Answer by michaelcarniol (score 2, accepted)

https://quant.stackexchange.com/a/34246

See Kandel and Pearson (1995) and Kim and Verrecchia (1991, 1994, 1997).

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