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: enter image description here and enter image description here 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: enter image description here

Looking closer at the formula for $\omega$, we see that it depends on some $q_{max}$ parameter. enter image description here

What I can't answer for myself is the question whether $q_{max}$ is heuristically chosen or is it estimated by some established method.


2 Answers 2


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.

  • $\begingroup$ which book was it? Is there any other books or resources that you could recommend as an intro to the practical realities? Thanks! $\endgroup$ Commented Sep 2, 2021 at 16:05
  • $\begingroup$ I believe it was "Option Trading" by Euan Sinclair, full text available here procapital.mohdfaiz.com/books/books-image/mainBook/… In my limited experience, I think it's better to build from trial-and-error and data. The theory doesn't really translate very well to actual trading. $\endgroup$
    – cjm2671
    Commented Sep 3, 2021 at 10:30

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.

  • $\begingroup$ This is more of a comment than an answer, no? $\endgroup$ Commented May 7, 2021 at 10:20
  • $\begingroup$ Actually after reading this again the OP seems correct, Qmax is like he said the max number of shares. I think the +1 is just to allow Qmax to go to 0 without breaking the formula (amount 1 assumed too small to matter). $\endgroup$
    – Projenix
    Commented Sep 10, 2021 at 15:00

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.