Choosing the Inventory Limit in the Avellaneda–Stoikov Market-Making Model
Summary
The document asks how to interpret the maximum inventory parameter in the infinite-horizon Avellaneda–Stoikov market-making model. The response describes it as a chosen cap on inventory, intended to limit how large a position the market maker can accumulate, including when incoming orders are adversely selected. It presents the parameter as a risk-control choice tied to the inventory exposure the agent is willing to accept, rather than identifying an established estimation procedure.
The answer offers implementation experience as context and cautions that the model idealizes important trading conditions: order arrivals follow an assumed distribution, exchange connectivity is perfect, and the strategy is always at the front of the queue. Those assumptions can make simulated or theoretical performance difficult to reproduce in live high-frequency market making. The exchange does not resolve how a practitioner should calibrate the cap for a particular instrument, capital base, or risk tolerance, and another brief reply disputes the question's formula interpretation without providing a resolution.
Key ideas
- The maximum inventory parameter represents a cap on the market maker's position.
- The cap is selected according to the inventory exposure the agent is willing to carry.
- Limiting inventory can reduce the risk of accumulating a large position under adverse selection.
- The model's assumed order flow, connectivity, and queue priority may differ from live trading.
- The document gives no established calibration method for choosing the cap.
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# Infinite horizon agent in Avellaneda-Stoikov model
# Infinite horizon agent in Avellaneda-Stoikov model
I am trying to understand the Avellaneda-Stoikov model for high frequency trading, in particular the optimizing agent with infinite horizon.
The reservation ask/bid prices for such an agent are defined in the paper as: and It is said in the paper that $\omega$ serves as an upper bound on the inventory position.
I took the argument of the natural logarithm from the reservation bid price and wrote the inequality satisfying the logarithm:
Looking closer at the formula for $\omega$, we see that it depends on some $q_{max}$ parameter.
What I can't answer for myself is the question whether $q_{max}$ is heuristically chosen or is it estimated by some established method.
## Answer by cjm2671 (score 8)
https://quant.stackexchange.com/a/41837
I'm doing this from memory, but as I recall $q_{\text{max}}$ is the maximum inventory on any side that you wish to take (otherwise you might build up a huge position if you are adversely selected).
Later papers such as this one https://arxiv.org/pdf/1105.3115.pdf helped my understanding.
As it actually happens, I implemented these algorithms and had a go doing HFT style MM on Bitmex. Although they do work in certain situations, I'll paraphrase something Sinclair wrote in his book, "Making money market making is trivial. Keeping it is a lot harder." These algos are an interesting starting point, but remember they are based on an idealised distribution of incoming orders, perfect connectivity to the exchange, and always being front-of-the-queue.
## Answer by Projenix (score 0)
https://quant.stackexchange.com/a/63808
if qmax here is a number of shares then qmax+1 does not make any sense to me whatsoever. I think that you have something wrong here.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.