Estimating the price impact of trades in a high-frequency microstructure model with jumps

We estimate a general microstructure model of the transitory and permanent impact of order flow on stock prices. Jumps are detected in both the transaction price (observation equation) and fundamental value (state equation). The model's parameters and variances are updated in real time. Prices can be altered by both the size and direction of trades, and the effects of buy-initiated and sell-initiated trades are different. We estimate this model using tick-by-tick data for 12 large-capitalization stocks traded on the Euronext-Paris Bourse. We find that, at tick frequency, the overnight return, the intraday jumps, and the continuous innovations represent approximately 7%,8.5%, and 36.7% of the total variation of stock returns. The microstructure model explains on average 47.7% of the total variation. Once jumps are filtered and parameters are estimated in real time, we also find that the price impact of trades is symmetric on average. However, the price of highly liquid stocks with a large proportion of sell-initiated orders tends to be more sensitive to buy trades, whereas the price of less liquid stocks with a large proportion of buy-initiated orders tends to be more sensitive to sell trades.