Why Market-Making Models Use a Terminal Inventory Constraint

Summary

The document explains the use of a terminal time in market-making models, where the market maker is required to liquidate inventory by a specified horizon. One motivation is mathematical: imposing a boundary condition can make a constrained optimization problem easier to solve and yield tractable analytical results. In this account, the modeling choice is often driven by solvability rather than by a universal operational rule.

A practical justification is that carrying no inventory overnight can reduce exposure to a prime broker and may support lower margin requirements or larger credit arrangements. Flattening positions can therefore reduce the capital tied up and support trading activity. The discussion does not claim that all market makers must end every session flat, or that the horizon always represents the market close. Whether the constraint is realistic depends on the trader’s financing arrangements, risk limits, and operating practices.

Key ideas

• A terminal inventory constraint can make market-making optimization problems easier to solve.
• The modeling horizon may be a mathematical convenience rather than a universal market rule.
• Flattening positions overnight can reduce credit exposure to a prime broker.
• Lower overnight inventory may affect margin needs and available trading capacity.

Tags

# What is the reasoning behind 'terminal time' in market making literature?


# What is the reasoning behind 'terminal time' in market making literature?












Market making literature and models often include a factor for 'terminal time' (1), (2) within which the market maker's inventory is liquidated.

What is the reasoning behind this idea? Is it simply to deal with close of market, or is there some other unwritten rule?

(1) http://stanford.edu/class/msande448/2018/Final/Reports/gr5.pdf

(2) https://arxiv.org/pdf/1602.00358.pdf

## Answer by madilyn (score 7, accepted)

https://quant.stackexchange.com/a/44166

The real reason for the literature you're seeing is that constrained optimization problems are often much easier to solve and give rise to simpler, more elegant results or tractable analytical solutions. It's entirely a mathematical motivation, not a practical one.

The "cop-out" reason (which is not completely invalid) they give to justify the terminal constraint is that: As a market maker, you generally want to have low margin requirements or large credit arrangements with your prime broker(s). This way you require less operating capital, and you can leave more orders open and generally increase your trading volume. You pose a much lower credit risk to your prime broker(s) when you carry no risk or positions overnight, so many market makers seek to flatten their positions before end of day.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.