Inventory Control and Quote Optimization in Market Making
Summary
The document discusses coordinating two high-frequency agents that trade opposite sides of a market while managing inventory and exposure limits. It frames market making as a control problem in which quotes must balance expected execution quality against the risk of holding a position. The cited model combines a diffusive fair-price process, representing market risk, with a point process for fills whose intensity declines as quotes move farther from fair value. A stochastic control framework then adjusts bid and ask distances to manage this trade-off.
A second response recommends defining maximum single-position and net-exposure constraints, then enforcing them through the strategy and order-management system. The discussion points toward established inventory-risk models and practical limits, but does not prescribe random order timing, queue placement, or how many orders to place at one price. It also offers no empirical comparison or implementation details, so the material is an introduction to modeling and constraint design rather than a complete operating recipe.
Key ideas
- Market-making quotes can be optimized by balancing fill probability against inventory and price risk.
- A model can represent fair value as a diffusion and fills as a point process with quote-dependent intensity.
- Stochastic control can adjust bid and ask distances from fair value as conditions change.
- Position limits should define both maximum single-side size and maximum net exposure.
- An order-management system can enforce the strategy’s inventory and exposure constraints.
Tags
Full text
# Position management and market-making techniques # Position management and market-making techniques Suppose, there is a HF strategy (agent) that is based on order book microstructure, and it is able to make good executions locally. More formally, in average its execution price is better than asset price $\tau$ sec. after the execution. Suppose, we manage two such agents: one for long orders, another for short orders. The question is how to develop a controller that synchronizes between two and manages their mutual position given position limit `N` on each side, and maximal order size `n`. I assume, this is a very broadly studied problem, especially among market makers. Can you please recommend relevant articles and ideas that provide overview of this topic and most sophisticated approaches. I'm especially interested in the very details such as: 1) Timing. is it prudent to generate random time intervals between last execution and new orders placement? 2) Pricing. How many orders can be executed on the same price? Thank you. ## Answer by lehalle (score 12, accepted) https://quant.stackexchange.com/a/7203 This paper Dealing with the Inventory Risk. A solution to the market making problem, has a full bibliography and explains the intra day market making mechanism. The model is made of two components: - a diffusion of the fair price (to model the market risk) - a point process (with an intensity in $A \exp -k \delta$ (where $\delta$ is the distance to the fair price) to model the probability to be hit once you choose quote price Then a stochastic control framework is set up to continuously adjust the quotes: distances (bid / ask) to the faire price. Thanks to a tricky change of variable, the problem is solved. ## Answer by Matt Wolf (score 3) https://quant.stackexchange.com/a/7192 You first need to clearly define your constraints first: - max single position size - max net exposure I am not sure why you want to limit order size. The whole idea of hft strategies is to maximize turnover. As long as your strategy generates alpha you should allow it to trade as often as the strategy prescribes. All you need to then do is to constrain the strategy and OMS to adhere to your position and exposure limits.
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