Automated Trader: What prompted you to explore the significance and influence of volume and its interaction with trader behaviour?
Leilei Shi: Well, it is relevant to our research background and the price-volume probability wave 1 equation I developed in an earlier paper, "Does security transaction volume-price behavior resemble a probability wave?". That earlier paper was in turn inspired by George Soros' book The Alchemy of Finance, which made me wonder whether it was possible to derive a wave equation for the stock market.
In the course of attempting to derive the equation, I discovered that liquidity levels directly drove the joint behaviour of volume and price, as well as how volume was distributed across a price range. Where price was volatile upward and downward on a daily basis, accumulated trading volume would show kurtosis 2 around a price mean value (for a practical illustration of this based on a stock price history, see Figure 1.)
From this analysis it was eventually possible to derive a price-volume probability wave equation and obtain a closed form solution 3 for the volume distribution.
Automated Trader: Can you explain the assumptions behind the price-volume probability wave equation?
The fundamental assumption is the existence of a trading liquidity utility expressed in terms of accumulated trading wealth. It is the rate of liquidity, similar to power or the rate of work in physics, which we term liquidity energy.
We divide the liquidity utility into two parts:
• The trading momentum utility, which is the momentum energy that drives the distribution of momentum
• The supply/demand imbalance utility, which is the potential energy that produces reversal forces in states of stationary equilibrium as they occur in the market.