We propose new methods for estimating the bid-ask spread from observed transaction prices alone. Our methods are based on the empirical characteristic function instead of the sample autocovariance function like the method of Roll (1984). As in Roll (1984), we have a closed form expression for...

The so-called leverage hypothesis is that negative shocks to prices/ returns affect volatility more than equal positive shocks. Whether this is attributable to changing financial leverage is still subject to dispute but the terminology is in wide use. There are many tests of the leverage...