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High-frequency market-making with inventory constraints and directional bets

Pietro Fodra 1 Mauricio Labadie 2, *
* Corresponding author
2 Quantitative Research
EXQIM - EXclusive Quantitative Investment Management
Abstract : We extend the market-making models with inventory constraints of Avellaneda and Stoikov ("High-frequency trading in a limit-order book", Quantitative Finance Vol.8 No.3 2008) and Gueant, Lehalle and Fernandez-Tapia ("Dealing with inventory risk", Preprint 2011) to the case of a rather general class of mid-price processes, under either exponential or linear PnL utility functions, and we add an inventory-risk-aversion parameter that penalises the marker-maker if she finishes her day with a non-zero inventory. This general, non-martingale framework allows a market-maker to make directional bets on market trends whilst keeping under control her inventory risk. With this inventory-risk-aversion parameter, the market-maker has not only direct control on her inventory risk but she also has indirect control on the moments of her PnL distribution. Therefore, this parameter can be seen as a fine-tuning of the marker-maker's risk-reward profile. In the case of a mean-reverting mid-price, we show numerically that the inventory-risk-aversion parameter gives the market-maker enough room to tailor her risk-reward profile, depending on her risk budgets in inventory and PnL distribution (especially variance, skewness, kurtosis and VaR). For example, when compared to the martingale benchmark, a market can choose to either increase her average PNL by more than 15\% and carry a huge risk, on inventory and PNL, or either give up 5\% of her benchmark PNL to increase her control on inventory and PNL, as well as increasing her Sharpe ratio by a factor bigger than 2.
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Contributor : Mauricio Labadie <>
Submitted on : Tuesday, June 19, 2012 - 10:48:51 AM
Last modification on : Wednesday, December 9, 2020 - 3:14:52 PM
Long-term archiving on: : Thursday, September 20, 2012 - 2:25:36 AM


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  • HAL Id : hal-00675925, version 5


Pietro Fodra, Mauricio Labadie. High-frequency market-making with inventory constraints and directional bets. 2012. ⟨hal-00675925v5⟩



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