Measuring Immediate Price Impact: The Comparison Between Different Price Impact Models


30 August 2014

As a consequence of the recent technological advances and proliferation of algorithmic and high-frequency trading, the cost of trading in financial markets has irrevocably changed. One important change relates to how trading affects prices, known as price impact. We compare different immediate price impact models for individual trades using out-of-sample predictions. Besides employing several parametric price impact models proposed in the literature, this paper introduces a novel semi-parametric approach, known as Generalised Additive Models, to estimate price impact. Using an Australian dataset, we find that the semi-parametric models outperform all other models both in- and out-of-sample. While the dependence of price impact on trading volume is consistent with a power-law function, nonlinearities between price impact and market capitalisation and volatility are much more complicated than what is suggested by the literature. *

This paper focuses on the models that measure the price impact immediately caused by individual trades. We are motivated by the fact that studying price impact at individual transaction level enables a deeper understanding of the relationship between price impact and trade characteristics compared to studying at aggregate transaction levels.

In addition, the impact that an intended transaction has on prices right after its execution is of greater relevance to a trader than the impact caused by trades aggregated during some time period over which the trader has no control. Ultimately, more accurate price impact models will give traders a better understanding of the costs of trading and therefore also facilitate the execution of their trades with minimal cost.

Conclusions and future research

This paper makes comparisons between various immediate price impact models for individual trades using bottom and second bottom groups of 20 stocks on the S&P/ASX 200 index. Besides the parametric frameworks that have been proposed in the literature, this paper introduces several semi-parametric and nonparametric settings in the family of Generalised Additive Models to estimate market impact.

We find that the semi-parametric model that employs price impact normalised by its average value as dependent variable, and takes into account the time of the day and day of the week, outperforms all parametric models that have been proposed in the literature based on Root Mean Squared Error (RMSE) or Mean Squared Error (MSE) criterion.

This superiority is obtained both for both stock groups and for both buys and sells during in-sample and out-of-sample periods. We further show that both the inherent flexibility of nonparametric models in fitting the data combined with the use of new explanatory variables contributes to the outperformance of the semi-parametric model.

Consistent with previous studies, we observe the nonlinear reliance of immediate price impact on trading volume, market capitalisation and volatility. While the power-law relationship between price impact and trading volume suggested in the literature is a reasonable specification, we show that the dependence of price impact on market capitalisation and volatility is far more complicated than a simple power-law function suggested by the existing literature.

Our study extends prior literature on price impact modelling by highlighting the use of semi-parametric and nonparametric frameworks with appropriate normalisation techniques as a good way of estimating and forecasting price impact. We also provide the first comprehensive analysis of out-of-sample forecasting for different price impact models.

Given that accurately quantifying price impact, which is the biggest component of total trading costs, is of great concern to any market participants and fund managers, our findings also have significant implications for traders and fund managers.

In this paper, we examine the immediate price impact of a trade. Recent studies show that price impact exhibits temporal characteristics. That is, the execution of a trade will impact prices of subsequent trades and may move prices to a new equilibrium. Using nonparametric techniques to model temporal or permanent price impact will be an important and interesting question for future researchers.

*This research was also supported by an Australian Research Council Linkage Grant.