We develop a financial market trading model in the tradition of Glosten and Milgrom (1985) that allows us to incorporate nontrivial volume. We observe that in this model price volatility is positively related to the trading volume and to the absolute value of the net order flow (i.e., the order imbalance). Moreover, higher volume leads to higher order imbalances. These findings are consistent with well-established empirical findings. Our model further predicts that higher trader participation and systematic improvements in the quality of traders’ information lead to higher volume, larger order imbalances, lower market depth, shorter duration, and higher price volatility.

When a company goes public, it is standard practice that the underwriting syndicate allocates more shares than are issued. The underwriter thus holds a short position that it commonly fills by aftermarket trading when market prices fall or, when prices rise, by executing the so-called overallotment option. This option is a standard feature of initial public offering (IPO) arrangements that allows the underwriter to purchase more shares from the issuer at the original offer price. We propose a theoretical model to study the implications of this combination of short position and overallotment option on the pricing of the IPO. Maximizing the sum of both the profits from their share of the offer revenue and the potential profits from aftermarket trading, we show that underwriters strategically distort the offer price. This results either in exacerbated underpricing when favorably informed underwriters lower prices to secure a signaling benefit, or in informationally inefficient offer prices when underwriters pool in offer prices irrespective of their information.