Over the Counter Market Making

In the former, we consider the problem of a trading desk which is faced with a
stochastic inflow and needs to unwind on the lit market while minimising trading costs.
The major novelty is that the inflow has an unobserved drift, interpreted as the toxic
component of flow, which reacts to the trader's unwind trades in a general linear
fashion. The problem is formulated as a partially observable stochastic control problem
and solved with a two-step approach. First, so-called filtering processes are derived for
a general unwind strategy, which are the best estimate of the toxic component of flow.
Second, having converted the problem into a classical fully observable stochastic
control problem posed in terms of the filtering processes, we use a variation method to
solve for the optimal unwind strategy. We then run numerical simulations and analyse
the model. Such a problem has applications to large market makers who wish to
internalise order flow to minimise firm wide trading costs.
The latter paper considers a variation of the classical market making problem. In
particular, the probability that orders placed within the market are filled by the market
maker depends on the quotes oOered by other market makers. We model the
competition's quotes in a reduced form manner as a function of trades missed by the
reference market maker. In doing so, the problem is considerably simpler than a game theoretic one, and we provide an endogenous motivation for the reference market
maker to consider the impact of missed trades. We use stochastic control techniques
find the optimal quotes in feedback form and find an approximate closed-form solution
under an assumption which we show to hold for a wide range or realistic model
parameters. This assumption is also motivated by previous works in the literature. We
show that the approximate closed-form solution performs almost exactly as well as the
solution found using an Euler scheme, and comfortably outperforms a state-of-the-art
deep reinforcement learning algorithm.
Future work is likely to focus on a variety of other relevant problems faced by market
makers. Example problems of interest include further research on optimal quoting,
optimal market making of assets other than equities, applications of cutting-edge
machine learning - including deep reinforcement learning - techniques to otherwise
intractable market making problems, optimal management of hedges within market
making and more. The mathematical methods used to solve these kinds of problems
include stochastic control, stochastic filtering, finite-player stochastic diOerential game
theory, techniques from financial mathematics including arbitrage theory, and machine
learning techniques including deep reinforcement learning and generative models