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

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