Using a large sample of limit orders on NYSE stocks, we find that investors submit more limit orders with even-eighth prices than odd-eight prices. However, even though there are a greater number of even-eighth limit orders, the proportion of executing limit orders submitted with even prices is greater than those submitted with odd prices for a large portion of our sample. We find that clustering on even prices is a positive function of stock price and various proxies for the dispersion in investors’ reservation prices. The preference for even prices affects stock quotes: Investors are more likely to submit a quote improving limit order if the limit price is even and quoted depth is higher for even quotes than for odd quotes.

We examine the effects of an order cancellation fee on limit order flow and execution quality in the PHLX options market. The cancellation fee on professional order flow effectively reduces the rate at which limit orders are canceled. Whereas the cancellation fee discourages the submission of nonmarketable orders, it encourages the submission of marketable orders. Consequently, nonmarketable order fill rates increase; marketable order fill speeds decrease; and bid-ask spreads widen. We also find slight increases in both dollar volume and market share.

We investigate the relations between trading-conveyed private information and stock return distributions. Using high-frequency measures of private information, we find that private information in trades is associated with lower stock return synchronicity. We also find private information in trades is positively associated with stock price crashes and positive stock price jumps. Our results are robust to several specification checks, including the use of alternative private information proxies, various model specifications, and different time periods. Overall, we demonstrate that trading conveyed private information reduces stock return synchronicity and predicts the frequency of crashes and jumps. Our findings can be useful for market makers, regulators, and traders, who are interested in firm-specific return variation and extreme stock price movements at high frequencies.

We examine whether options exchanges’ pricing schedules affect broker order routing behavior and limit order execution quality. We find that some brokers seemingly maximize the value of their order flow by selling marketable orders and sending nonmarketable orders to exchanges that offer large liquidity rebates. Other brokers appear to bypass liquidity rebates by routing both marketable and nonmarketable orders to exchanges that purchase order flow. Using a decision by the Philadelphia Stock Exchange (PHLX) to change its trading protocol, we provide empirical evidence that brokers can enhance limit order execution quality by routing nonmarketable limit orders to options exchanges that purchase order flow.

Consistent with prior literature, we find that average relative effective spreads are higher for venues that pay for order flow (PFOF) than for venues utilizing the maker-taker (MT) model. This relation becomes more nuanced when liquidity fees are incorporated into liquidity cost measures. For the majority of options, PFOF venues offer lower average liquidity costs net of taker fees. Net liquidity costs for the high-priced options, however, are lower for MT venues. Overall, our results suggest that the inclusion of fees and rebates can rationalize the routing of most, but not all, marketable orders to PFOF venues.

We study odd-lot trading and determine if an odd-lot trade results from odd-lot orders or if odd-lots are a result of orders broken into multiple trades. We confirm that odd-lot transactions contribute to price discovery. Our finding that odd-lot transactions contain substantial information is not being driven by orders that are originally larger than 100 shares and subsequently divided into odd-lot transactions. We further find that odd-lot transactions resulting from odd-lot orders add more to price discovery than odd-lot transactions resulting from orders for 100 or more shares. Additionally, we find that more price contribution occurs when non-high frequency traders trade in an odd-lot transaction.

Ellis et al. [Ellis, K., Michaely, R., O’Hara, M., 2000. The accuracy of trade classification rules: Evidence from Nasdaq. Journal of Financial and Quantitative Analysis 35 (4), 529–551] find that trade classification rules have limited success in classifying trades which execute inside the quotes. We reconfirm this result and propose an alternative algorithm to improve the classification accuracy for trades inside the quotes. This alternative algorithm improves the overall success rate for classifying trades, especially for trades that occur inside the quotes. Additionally, we show that the Lee and Ready [Lee, C., Ready, M., 1991. Inferring trade direction from intraday data. Journal of Finance 46, 733–747] and Ellis et al. (2000) trade classification algorithms provide biased estimates of the actual effective spreads and price impacts, while our algorithm provides statistically unbiased estimates of actual effective spreads and price impacts.