# Bid-Ask spread in Roll's model: Negative autocovariance of returns and informational content

Currently studying on techniques to estimate the bid-ask spread. Perhaps the most widely known model is the Roll model (1984). Let $$P_t$$ indicate log prices

$$\begin{cases} Bid_t=P_t-c, \\ Ask_t=P_t+c, \end{cases}$$

Where $$c=\sqrt{-Cov(\Delta P_t, \Delta P_{t-1})}$$.