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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?

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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:

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  • $\begingroup$ 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! $\endgroup$ – Federico Caccia May 3 at 14:18

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