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Keywords:
market maker; optimal decision; price and inventory; high frequency data; dynamic model
market maker; optimal decision; price and inventory; high frequency data; dynamic model
Summary:
We model a market with multiple liquidity takers and a single market maker maximizing his discounted consumption while keeping a prescribed probability of bankruptcy. We show that, given this setting, spread and price bias (a difference between the midpoint- and the expected fair price) depend solely on the MM's inventory and his uncertainty concerning the fair price. Tested on ten-second data from ten US electronic markets, our model gives significant results with the price bias decreasing in the inventory and increasing in the uncertainty and with the spread mostly increasing in the uncertainty.
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