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

## TL;DR

This paper introduces a dimensionality reduction method using factor models for multi-asset OTC market making, incorporating variable transaction sizes and price responses, to overcome computational challenges.

## Contribution

It proposes a novel factor-based dimensionality reduction technique for multi-asset market making models with variable transaction sizes.

## Key findings

- Effective reduction of model complexity in multi-asset settings
- Inclusion of variable transaction sizes enhances model realism
- Improved computational efficiency for market making optimization

## Abstract

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.