The measures of the spread discussed above require observations on transaction prices and bid–ask quotes. Very often, however, quoted prices are either unavailable, unreliable or difficult to handle. As noted, quotes may not be binding or the spread may vary in the course of the trading day, so estimation of the spread based on transaction prices is usually preferred. Roll (1984) offers a very parsimonious model for estimating spread, using the time series of the prices at which trades were made. This model shows that when transaction costs consist of order processing costs only, i.e. in the absence of both adverse selection and inventory costs, the quoted spread coincides with the realized spread.

Roll demonstrates that it is possible to estimate spread by computing the autocovariance of transaction prices. Below we show how in the absence of transaction costs this auto-covariance is equal to zero, whereas with transaction costs, it is negative and a function of the spread. This allows us to estimate the spread by using transaction prices alone. This method proves useful when quoted bid and ask prices are not available.