I'm working in the Avellaneda-Stoikov implementation using Python. My implementation reproduces the authors' results, but I don't know how to properly adapt the algorithm in order to consider a larger time horizon. From the equation

r = s - q * gamma * sigma**2 * (T-t)

if we use larger T, the indifference price computed could become too big compared with the mid price s, or even a negative value, when q is positive.

Is there an a-dimensional implementation? How to independize from T? Is there a possibility to independize also from the election of s?


1 Answer 1


In Dealing with the inventory risk: a solution to the market making problem (preprint available at arxiv) we extend the approximation proposed by Marco and Sasha to a rigorous mathematical framework and provide exact steady-state approximation. The bid-ask spread that should be quoted is

$$\psi(q;k,\gamma):=-\frac{1}{k}\ln\frac{f^0_{q-1}f^0_{q+1}}{(f^0_{q})^2}+\frac{2}{\gamma}\ln\frac{\gamma+k}{k},$$ where $k$ is a characteristic of the liquidity consuming flow, $\gamma$ is the MM risk aversion, and the $f^0_q$ are solution of the steady-state version of the ODE driving the value of accepting an inventory of $q$.

The paper explain all this and has been followed by some others. I especially recommend the ones driven by the two other authors:

  • $\begingroup$ Thanks for your response @lehalle, since I lack quant background it was difficult to me to understand the paper you refer, but I will give it another try, trying to focus on the topics you mention. Thanks! $\endgroup$ Commented May 3, 2020 at 14:18

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.