High-frequency market-making with inventory constraints and directional bets
Résumé
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. In the case of a mean-reverting mid-price, we show numerically that the market-maker can increase her PnL between 10% and 25% depending on her budget or tolerance on risks in inventory and PnL distribution (especially variance, skewness, kurtosis and VaR). Moreover, 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.
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