I am trying to reconstruct the limit order book from the NASDAQ Historical TotalView -ITCH data. After I decode the raw data, I can successfully generate whole messages flow from ITCH data. However,in the messages flow there are some limit price buy order which has bid price higher than the current best ask price on the LOB, same as the limit price sell order which has ask price lower than the current best bid price. I just wondering how can I deal with this type of messages during the reconstructing LOB, since if I just directly update these limit orders, in the LOB the best bid price will be higher than the best ask price which doesn't make any sense to me. I find online, these type of the messages seems are market price order.
Right now I only consider messages with type: T,S,A,F,E,C,X,D,U,P
Thank you so much
