Interpreting Drift Parameters in Inventory-Risk Market Making
Summary
The question concerns implementing the drift extension to an inventory-risk market-making model associated with Gueant, Lehalle, and Tapia. The author can reproduce the standard model and its published surfaces, but is unsure about signs in a matrix term and how to normalize a signal parameter linked to beta. They also ask whether execution policies should react to changing signals to reduce adverse selection.
The brief answer refers to a paper example to interpret a parameter value: it says a value of 0.98 represents an expected 2% price decrease and that the parameter should remain positive. It tentatively agrees that the matrix signs should be positive, while explicitly expressing uncertainty and offering no derivation. The response does not resolve normalization in general, analyze signal-aware requoting, or recommend an optimal execution policy. Its parameter interpretation is therefore a narrow pointer, not a complete implementation guide or validated treatment of the model’s sign conventions.
Key ideas
- The drift extension adds a signal-related term to an inventory-risk market-making model.
- The answer interprets a parameter value of 0.98 as encoding an expected 2% price decrease.
- The response tentatively endorses positive matrix signs but provides no mathematical derivation.
- The exchange leaves signal-aware execution and requoting policy questions unresolved.
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Full text
# Dealing with the inventory risk: solution with drift # Dealing with the inventory risk: solution with drift I'm implementing the solution with drift from "Dealing with the inventory risk" from Gueant, Lehalle and Tapia. I'm using the link https://arxiv.org/pdf/1105.3115.pdf as reference. I can reproduce the standard solution with no issues, and then reproduce the surfaces in the paper. I'm trying now to implement the solution with drift, which is very similar to the standard solution, with a new component beta being added to the matrix M. However when looking at the answer, I see a plus sign that is counterintuitive to me. This first appears in the proposition 4: However the signs in the new matrix M doesn't exactly match the propositon 4: Real apologies if I'm making a pointless case here. I don't have a formal training in mathematics but this supposed inconsistency really bugged me and I had no one else to ask. Moreover, I would like to ask a few more questions: 1 - How should u (since beta = kappa * u) be properly normalized? 2 - Lehalle commented in another post that https://stanford.edu/class/msande448/2018/Final/Reports/gr5.pdf is a good basis of an implementation. However, in the incorporation of trading signals, it seems intuitive to me that the markov chain which is basis for the execution policy should be updated to incorporate the change of signals to perhaps trigger a requote (and thus avoid adverse selection). I read https://deanstreetlab.github.io/papers/papers/High%20Frequency%20Trading/High%20Frequency%20Market%20Making%20-%20Optimal%20Quoting.pdf which more or less provides a solution, although the framework is very different from "Dealing with the inventory risk". Are there papers around this topic? If no, which execution strategies would be optimal? ## Answer by sandstorm111 (score 0) https://quant.stackexchange.com/a/75778 Following the footnotes of example in page 25 of the paper https://arxiv.org/pdf/1206.4810.pdf: 1 - u = 0.98 means an expectation in 2% decrease in price, so u should be always positive. The signs should be + nor - in the matrix. Though I do not have enough patent to declare this for sure, since I have absolutely no formal training in math.
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