Size matters for OTC market makers: general results and dimensionality reduction techniques

Philippe Bergault (1) , Olivier Guéant (1)

1 CES - Centre d'économie de la Sorbonne

In most OTC markets, a small number of market makers provide liquidity to other market participants. More precisely, for a list of assets, they set prices at which they agree to buy and sell. Market makers face therefore an interesting optimization problem: they need to choose bid and ask prices for making money while mitigating the risk associated with holding inventory in a volatile market. Many market making models have been proposed in the academic literature, most of them dealing with single-asset market making whereas market makers are usually in charge of a long list of assets. The rare models tackling multi-asset market making suffer however from the curse of dimensionality when it comes to the numerical approximation of the optimal quotes. The goal of this paper is to propose a dimensionality reduction technique to address multi-asset market making by using a factor model. Moreover, we generalize existing market making models by the addition of an important feature: the existence of different transaction sizes and the possibility for the market makers in OTC markets to answer different prices to requests with different sizes.

Mots clés: Market making; Stochastic optimal control; Curse of dimensionality; Integro-dierential equations; Risk factor models

Domaines: Finance quantitative [q-fin.CP]

Philippe Bergault, Olivier Guéant. Size matters for OTC market makers: general results and dimensionality reduction techniques. 2020. ⟨hal-02987894⟩