  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.
