Thanks for your comment Goomboo. Below are some papers that discuss how liquidity and volatility are related. Specifically look at ¶ 1.3 of the first paper, "An empirical behavioral model of liquidity and volatility," by Szabolcs Mike and J. Doyne Farmer ("Szabolcs et al.").http://www.sciencedirect.com/science/article/pii/S0165188907000450http://www.fednewyork.org/research/economists/sarkar/sarkar_locke.pdf
An illiquid market merely means that the commodities, securities, buyers, etc. are more scarce. When there are "lots" of products and buyers, the price movement from one transaction to the next is very smooth. The inverse is also true, when there are relatively few products or buyers, the price movement can become erratic.
Often there must be some amount of trading for many people to notice volatility, however, your equation is over simplified. In finance volatility is usually calculated using stochastic models (http://en.wikipedia.org/wiki/Stochastic_volatility
). Furthermore, the instant volatility that TDAmeritrade integrates into both its consumer trading platform and API uses option spreads as the input. The idea behind the TDAmeritrade model is that options become more valuable as volatility rises. This is exemplified in the VIX, as the "fear factor" increases, people leave the market. The market becomes less liquid as the demand for the security can vary greatly thoughout any given period of time because there are fewer players, and thus volatility increases (see also VIX the "fear index" http://en.wikipedia.org/wiki/VIX
). The same is true on the upside, when a security becomes scarce and there is not a steady flow of shares/securities/goods to suit demand the price can move drastically, again giving rise to volatility.
I appreciation your comment and push back. I am currently writing a paper on this topic and you have definitely helped me create a stronger and well documented argument.