High-frequency market-making with inventory constraints and directional bets
Résumé
In this paper 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 Lehalle, Gueant and Fernandez-Tapia ("Dealing with inventory risk", Preprint 2011) to the case of a rather general class mid-price processes, under either exponential or linear PnL utility functions, and with 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 order to achieve this, the marker-maker places non-symmetric limit orders that favour market orders to hit her bid (resp. ask) quotes if she expects that prices will go up (resp. down). 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 buget risk on 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 risks on her PnL distribution (esp. the moments such as mean, variance, skewness and kurtosis, as well as her VaR) . Therefore, this parameter can be seen as a fine-tuning of the marker-maker's risk-reward profile.
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