Dealing with the Inventory Risk

Olivier Guéant (1) , Charles-Albert Lehalle (2) , Joaquin Fernandez Tapia (1)

1 LJLL - Laboratoire Jacques-Louis Lions
2 Head of Quantitative Research

Market makers have to continuously set bid and ask quotes for the stocks they have under consideration. Hence they face a complex optimization problem in which their return, based on the bid-ask spread they quote and the frequency they indeed provide liquidity, is challenged by the price risk they bear due to their inventory. In this paper, we provide optimal bid and ask quotes and closed-form approximations are derived using spectral arguments

Domaines: Analyse numérique [math.NA]

Olivier Guéant, Charles-Albert Lehalle, Joaquin Fernandez Tapia. Dealing with the Inventory Risk. 2011. ⟨hal-00628528⟩