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Medium · Market Microstructure · Quant Trader interview question · market-microstructure, spread-estimation, autocovariance, roll-model
A market maker in a high-frequency trading firm observes a stock whose price primarily bounces between the bid and ask prices. You're tasked with estimating the effective spread using Roll's model. Given the autocovariance of consecutive price changes, $Cov(\Delta P_t, \Delta P_{t-1})$, what is the formula for the effective spread, $s$, as defined by Roll?