High-frequency market-making with inventory constraints and directional bets
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 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 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). 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.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Potters, Marc & Bouchaud, Jean-Philippe, 2003. "More statistical properties of order books and price impact," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 133-140.
- Hans R. Stoll, .
"The Supply of Dealer Services in Securities Markets,"
Rodney L. White Center for Financial Research Working Papers
02-78, Wharton School Rodney L. White Center for Financial Research.
- Stoll, Hans R, 1978. "The Supply of Dealer Services in Securities Markets," Journal of Finance, American Finance Association, vol. 33(4), pages 1133-51, September.
- Hans R. Stoll, . "The Supply of Dealer Services in Securities Markets," Rodney L. White Center for Financial Research Working Papers 2-78, Wharton School Rodney L. White Center for Financial Research.
- Fabien Guilbaud & Huyen Pham, 2011. "Optimal High Frequency Trading with limit and market orders," Papers 1106.5040, arXiv.org.
- Fabien Guilbaud & Huyen Pham, 2011. "Optimal High Frequency Trading with limit and market orders," Working Papers hal-00603385, HAL.
- Ho, Thomas & Stoll, Hans R., 1981.
"Optimal dealer pricing under transactions and return uncertainty,"
Journal of Financial Economics,
Elsevier, vol. 9(1), pages 47-73, March.
- Thomas Ho & Hans Stoll, . "Optimal Dealer Pricing Under Transactions and Return Uncertainty," Rodney L. White Center for Financial Research Working Papers 27-79, Wharton School Rodney L. White Center for Financial Research.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1206.4810. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If references are entirely missing, you can add them using this form.