This workshop focuses on recent developments in Market Micostructure.

Schedule:

09:00-09:45 Marcel Nutz (Columbia University): Unwinding Stochastic Order Flow
09:45-10:30 Ben Hambly (University of Oxford): Order Books and SPDEs

10:30-11:00 Coffee Break

11:00-11:45 Basil Williams (Imperial Business School): Spoofing in Equilibrium
11:45-12:30 Eyal Neuman (Imperial): Fast and Slow Optimal Trading with Exogenous Information

12:30-14:00 Lunch Break

14:00-14:45 Xiaofei Shi (University of Toronto): Illiquidity, Interest Rates, and Asset Prices
14:45-15:30 Faycal Drissi (University of Oxford): Price Impact in Quote Driven Markets and Applications to AMM Design

15:30-16:00 Coffee Break

16:00-16:45 Johannes Muhle-Karbe (Imperial): Concave Cross Impact

Abstracts of the talks:

• Faycal Drissi (University of Oxford): Price Impact in Quote Driven Markets and Applications to AMM Design
  • In over-the-counter (OTC) markets,  liquidity providers propose quotes at which they are ready to buy or to sell  securities. This paper proposes a model for a large OTC market maker (LMM) who fills orders from informed and uninformed traders. The LMM uses the trading flow she receives and other sources of information to update her estimate of the fundamental price, which she cannot directly observe. To account for endogenous price formation, the LMM employs inventory-sensitive impact functions to update her estimate of the fundamental price following trades filled in her trading venue.  We solve the optimal market making problem in a finite and an infinite horizon setup. Finally, we show that the model can be used to generalise current designs of automated market makers where liquidity providers are currently providing liquidity at a loss, on average.
• Ben Hambly (University of Oxford): Order Books and SPDEs
  • Starting from some simple models for the limit order book, it is possible to take a scaling limit and arrive at a stochastic partial differential equation whuch describes the evolution of the whole book. We will consider SPDEs which are eitgher coupled versions of the stochastic heat equation or stochastic Stefan problems driven by white noise. I will discuss the mathematical issues that arise in these models.
• Johannes Muhle-Karbe (Imperial): Concave Cross Impact
  • The price impact of large orders is well known to be a concave function of trade size. We discuss how to extend models consistent with this “square-root law” to multivariate settings with cross impact, where trading each asset also impacts the prices of the others. In this context, we derive consistency conditions that rule out price manipulation, discuss how cross impact affects optimal trading strategies, and illustrate these results using CFM metaorder data.  (Joint work in progress with Natascha Hey and Iacopo Mastromatteo)
• Eyal Neuman (Imperial): Fast and Slow Optimal Trading with Exogenous Information
  • We model the interaction between an investor executing trades at low frequency and a high-frequency trader as a multiperiod stochastic  Stackelberg game. The high-frequency trader exploits price information more frequently and is subject to periodic inventory constraints.  We are able to explicitly compute the equilibrium strategies, in two steps. We first derive the optimal strategy of the high-frequency trader given any strategy adopted by the investor. Then, we solve the problem of the  investor given the optimal  strategy of the high-frequency trader, in terms of the resolvent of a Fredholm integral equation.  Our results show that the high-frequency trader adopts a predatory strategy whenever the value of the trading signal is high, and follows a  cooperative strategy otherwise. We also show that there is a net gain in performance for the investor  from taking into account the order flow of the high-frequency trader. A U-shaped intraday pattern in trading volume is shown to arise endogenously as a result of the strategic behavior of the agents. (Joint work with Rama Cont and Alessandro Micheli, Preprint)
• Marcel Nutz (Columbia University): Unwinding Stochastic Order Flow
  • We study how to unwind stochastic order flow with minimal transaction costs. Stochastic order flow arises, e.g., in the central risk book (CRB), a centralized trading desk that aggregates order flows within a financial institution. The desk can warehouse in-flow orders, ideally netting them against subsequent opposite orders (internalization), or route them to the market (externalization) and incur costs related to price impact and bid-ask spread. We model and solve this problem for a general class of in-flow processes, enabling us to study in detail how in-flow characteristics affect optimal strategy and core trading metrics. Our model allows for an analytic solution in semi-closed form and is readily implementable numerically. Compared with a standard execution problem where the order size is known upfront, the unwind strategy exhibits an additive adjustment for projected future in flows. Its sign depends on the autocorrelation of orders; only truth-telling (martingale) flow is unwound myopically. In addition to analytic results, we present extensive simulations for different use cases and regimes, and introduce new metrics of practical interest.  (Joint work with Kevin Webster and Long Zhao, Preprint)
• Xiaofei Shi (University of Toronto): Illiquidity, Interest Rates, and Asset Prices
  • This paper examines the effect of illiquidity on the dynamics of asset prices and interest rates. Equilibrium is identified by a system of coupled forward-backward stochastic differential equations, which admit explicit asymptotic solutions in the high-liquidity regime. Illiquidity increases price volatility and the risk premium but decreases the interest rate. (Joint work in progress with Paolo Guasoni and Johannes Muhle-Karbe.)
• Basil Williams (Imperial Business School): Spoofing in Equilibrium
  • We present a model of dynamic trading with exogenous and strategic cancellation of orders. We define spoofing as strategically placing and canceling orders in order to move prices and trade later in the opposite direction. We show that spoofing can occur in equilibrium, slowing price discovery and raising spreads and volatility. A novel prediction is that the prevalence of equilibrium spoofing is single-peaked in the measure of informed traders, suggesting that spoofing should be more prevalent in markets of intermediate liquidity. We also consider cross-market spoofing and discuss how regulators should allocate resources towards cross-market surveillance. (Joint work with Andrzej Skrzypacz, Preprint)