Academic Research on Ask

• Asset pricing and the bid-askspread, Amihud, Y., & Mendelson, H. (1986). Asset pricing and the bid-ask spread.Journal of financial Economics,17(2), 223-249. This paper studies the effect of the bid-ask spread on asset pricing. We analyze a model in which investors with different expected holding periods trade assets with different relative spreads. The resulting testable hypothesis is that market-observed expexted return is an increasing and concave function of the spread. We test this hypothesis, and the empirical results are consistent with the predictions of the model. 
• Pricefunctionals with bidaskspreads: an axiomatic approach, Jouini, E. (2000). Price functionals with bidask spreads: an axiomatic approach.Journal of Mathematical Economics,34(4), 547-558 In Jouini and Kallal [Jouini, E., Kallal, H., 1995. Martinagles and arbitrage in securities markets with transaction costs. Journal of Economic Theory 66 (1) 178-197], the authors characterized the absence of arbitrage opportunities for contingent claims with cash delivery in the presence of bidask spreads. Other authors obtained similar results for a more general definition of the contingent claims but assuming some specific price processes and transaction costs rather than bidask spreads in general (see for instance, Cvitanic and Karatzas [Cvitanic, J., Karatzas, I., 1996. Hedging and portfolio optimization under transaction costs: a martinangle approach. Mathematical Finance 6, 133-166]). The main difference consists of the fact that the bidask ratio is constant in this last reference. This assumption does not permit to encompass situations where the prices are determined by the buying and selling limit orders or by a (resp. competitive) specialist (resp. market-makers). We derive in this paper some implications from the no-arbitrage assumption on the price functionals that generalizes all the previous results in a very general setting. Indeed, under some minimal assumptions on the price functional, we prove that the prices of the contingent claims are necessarily in some minimal interval. This result opens the way to many empirical analyses. 
• Pricereversals, bid-askspreads, and market efficiency, Atkins, A. B., & Dyl, E. A. (1990). Price reversals, bid-ask spreads, and market efficiency.Journal of Financial and Quantitative Analysis,25(4), 535-547. We examine the behavior of common stock prices after a large change in price occurs during a single trading day and find evidence that the stock market appears to have overreacted, especially in the case of price declines; however, the magnitude of the overreaction is small compared to the bid-ask spreads observed for the individual stocks in the sample. We interpret this finding as being consistent with a market that is efficient after transactions costs are considered. 
• Minimumpricevariations, discrete bidaskspreads, and quotation sizes, Harris, L. E. (1994). Minimum price variations, discrete bidask spreads, and quotation sizes.The Review of Financial Studies,7(1), 149-178. Exchange minimum price variation regulations create discrete bidask spreads. If the minimum quotable spread exceeds the spread that otherwise would be quoted, spreads will be wide and the number of shares offered at the bid and ask may be large. A cross-sectional discrete spread model is estimated by using intraday stock quotation spread frequencies. The results are used to project$116$116spread usage frequencies given a$116$116tick. Projected changes in quotation sizes and in trade volumes are obtained from regression models. For stocks priced under $10, the models predict spreads would decrease 38 percent, quotation sizes would decrease 16 percent, and daily volume would increase 34 percent. 
• Bid,askand transaction prices in a specialist market with heterogeneously informed traders, Glosten, L. R., & Milgrom, P. R. (1985). Bid, ask and transaction prices in a specialist market with heterogeneously informed traders.Journal of financial economics,14(1), 71-100. The presence of traders with superior information leads to a positive bid-ask spread even when the specialist is risk-neutral and makes zero expected profits. The resulting transaction prices convey information, and the expectation of the average spread squared times volume is bounded by a number that is independent of insider activity. The serial correlation of transaction price differences is a function of the proportion of the spread due to adverse selection. A bid-ask spread implies a divergence between observed returns and realizable returns. Observed returns are approximately realizable returns plus what the uninformed anticipate losing to the insiders.