# 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.

1. 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?
2. 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.

• Once you have a rule for classifying each trade as buyer initiated (B) or seller initiated (S) you can indeed estimate Kyle's and similar models. – noob2 May 15 '17 at 20:40
• Recall that for every buyer, there is a seller. Thus it is not the volume (as your title implies) that affects price by your argument, but the imbalance between supply and demand. Whether the high trading volume is due to the demand or the supply side would determine the price going up vs. down. – Richard Hardy May 16 '17 at 16:26
• @Richard. It is also concievable that in the face of new information (eg an adverse data release), that both buyers and sellers might agree to transact at a different price, without necessitating a change in volume. Note that this effect can be in addition to, rather than in place of, the well stated arguement you made. – Yugmorf May 17 '17 at 0:57
• @Yugmorf, yes, of course there are more price changers than just the one I mentioned. – Richard Hardy May 17 '17 at 4:59