Optimal market making

Olivier Guéant (ENSAE ParisTech)
Thursday, November 19, 2015 - 5:15pm
HU Berlin, Rudower Chaussee 25, Room 1.115

Market makers provide liquidity to other market participants: they propose prices at which they stand ready to buy and sell a wide variety of assets. Market makers face a complex dynamical optimization problem. They need to propose bid and offer/ask prices in an optimal way for making money out of the difference between these two prices (their bid-ask spread), while mitigating the risk associated with price changes. In practice, market makers indeed seldom buy and sell simultaneously. Therefore, they hold long or short inventories and are exposed to market risk. In my talk, (i) I reconcile the different modelling approaches proposed in the literature since the publication of the seminal paper ''High-frequency trading in a limit order book'' by Marco Avellaneda and Sasha Stoikov, (ii) I prove new general results on the existence and the characterization of optimal market making strategies, (iii) I obtain new closed form and almost-closed form approximations for the optimal quotes, and (iv) I discuss multi-asset market making.