It stands for market best bid or best offer; the best bid or offer price on the simple order book on an exchange. The best price is usually associated with the possibility to display aggregate orders and quote size of contracts being traded. MBBO reflects the highest limit price of a resting, visible bid order and the lowest limit price of a resting, visible ask order, in exception of orders with minimum quantity restrictions (minimum quantity order constrains). Therefore, the execution price of an order/ a trade whose resting side would set a price out of the displayed/ visible MBBO is corrected to the highest price available within it.
In a corresponding context, MBBO may also denote many best bids and best offers (or many BBOs); the ability of an exchange to produce many best quotes, rather than the single market best bid or best offer.
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