A Continuous and Efficient Fundamental Price on the Discrete Order Book Grid

Abstract

This paper develops a model of liquidity provision in financial markets by adapting the Madhavan, Richardson, and Roomans (1997) price formation model to realistic order books with quote discretization and liquidity rebates. We postulate that liquidity providers observe a fundamental price which is continuous, efficient, and can assume values outside the interval spanned by the best quotes. We confirm the predictions of our price formation model with extensive empirical tests on large high-frequency datasets of 100 liquid Nasdaq stocks. Finally we use the model to propose an estimator of the fundamental price based on the rebate adjusted volume imbalance at the best quotes and we empirically show that it outperforms other simpler estimators.

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“…Unmatched orders await for execution in electronic records known as limit order books (LOBs henceforth). By submitting an order, traders pledge to sell (buy) up to a certain quantity of a given asset for a price that is greater (less) or equal than its limit price [2,54]. The submission activates a trade-matching algorithm which determines whether the order can be immediately matched against earlier orders that are still queued in the LOB [54].…”

“…By submitting an order, traders pledge to sell (buy) up to a certain quantity of a given asset for a price that is greater (less) or equal than its limit price [2,54]. The submission activates a trade-matching algorithm which determines whether the order can be immediately matched against earlier orders that are still queued in the LOB [54]. A matching occurs anytime a buy (sell) order includes a price that is greater (less) or equal than the one included in a sell (buy) order.…”

“…Orders that are completely matched upon entering into the system are called market orders. Conversely, orders that are partially matched or completely unmatched upon entering into the system (i.e., limit orders) are queued in the LOB until they are completely matched by forthcoming orders or deleted by their owners [54].…”

“…A very common scheme is the price-time priority rule which uses the submission time to set the priority among limit orders occupying the same price level, i.e. the order that entered the LOB earlier is executed first [54].…”