Optimal Liquidity Provision in Limit Order Markets
Christoph Kühn (Goethe University, Germany)
Joint work with Johannes Muhle-Karbe

Tuesday June 3, 11:00-11:30 | session 1.8 | Market Microstructures | room 1+2

A small investor provides liquidity at the best bid and ask prices of a limit order market. For small spreads and frequent orders of other market participants, we explicitly determine the investor's optimal policy and welfare. In doing so, we allow for general dynamics of the mid price, the spread, and the order flow, as well as for arbitrary preferences of the liquidity provider under consideration. The talk is based on arXiv:1309.5235

Does Hidden Liquidity Harm Price Efficiency? Equilibrium Exposure under Latent Demand.
Gökhan Cebiroglu (University of Vienna, Austria)

Tuesday June 3, 11:30-12:00 | session 1.8 | Market Microstructures | room 1+2

We develop a dynamic model of a limit order book market that competes for order flow with off-exchange trading mechanisms. Liquidity suppliers in the limit order book market face a trade-off between the costs and benefits of exposure. Because large exposed orders have the critical mass to elicit order flow from latent investors - in equilibrium - large traders expose their trading intentions. Exposure is mutually beneficent as it generates liquidity externalities and facilitates an efficient coordination of the supply and demand side of liquidity. Thus, it turns out that hidden liquidity can be the source of significant price inefficiencies. We derive a range of testable implications. First, markets with wider spreads and low (opposite-side) depth are 'hidden''; the role of the tick is ambiguous. Second, the use of critically large hidden orders induces price fluctuations and increases transaction costs. Importantly, these trading frictions do not arise from informational asymmetry but rather from the design and structure of trading. Our theory is put to test using both high-frequency order message and hidden liquidity data from NASDAQ.

Limit Order Books with Stochastic Market Depth
Steven Kou (National University of Singapore, Singapore)
Joint work with Chun Wang and Ningyuan Chen

Tuesday June 3, 12:00-12:30 | session 1.8 | Market Microstructures | room 1+2

We propose a model for limit order books with stochastic, reverse U-shaped, market depth, consistent with empirical studies. Stochastic market depth is necessary to accommodate various order activities, such as limit order submission at and outside the best quotes and order cancellation, which may account for a large proportion of limit order activities. To show the analytical tractability of the model, in addition to a dynamic programming formulation of the optimal execution problem, we provide easily computable and tight upper and lower bounds for the optimal execution cost, as well as their resulting trading strategies via quadratic programming and jump-linear-quadratic control.

Robust Market Making
Ryan Donnelly (University of Toronto, Canada)
Joint work with Ryan Donnelly and Alvaro Cartea

Tuesday June 3, 12:30-13:00 | session 1.8 | Market Microstructures | room 1+2

Because market makers (MMs) acknowledge that their models are incorrectly specified, in this paper, we allow for ambiguity in their choices to make their models robust to misspecification in (i) the arrival rate of market orders (MOs), (ii) the fill probability of limit orders, and (iii) the dynamics of the fundamental value of the asset they deal. We demonstrate that MMs adjust their quotes to reduce inventory risk and adverse selection costs. Moreover, robust market making increases the Sharpe ratio of market making strategies and allows for the MM to fine tune the tradeoff between the mean and the standard deviation of expected profits. Our framework adopts the robust optimal control approach of Hansen and Sargent (2007) and we provide analytical solutions for the robust optimal strategies as well as a verification theorem. We also find that in many circumstances ambiguity averse MMs act differently from MMs who are risk averse.
The MM's reference model consists of MOs arriving at Poisson times and upon their arrival, will hit/lift the MM's posted limit orders with a probability that decays exponentially as the MM post's deeper into the LOB. The mid-price moves as an independent Brownian motion and may jump at the arrival times of MOs to mimic the effect of immediate adverse selection impact. To account for ambiguity aversion, we allow the agent to consider alternative models whereby the underlying Poisson random measure which drives the arrival of MOs and fill probabilities, as well as the drift of the Brownian motion, can vary. The agent penalizes candidate models with relative entropy and solves the resulting robust stochastic optimal control problem. We provide several analytical results, characterize the optimal behaviour of the MM and show the equivalence between ambiguity in drift and inventory penalization. Furthermore, we demonstrate how the MM may improve their risk-reward by accounting for the fact that their model is only an incorrect reflection of reality.