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edited Dec 18, 2022 at 15:59

in our extension of Avellaneda - Stoikov paper, we provide some numerical examples: Dealing with the Inventory Risk. A solution to the market making problem.

For this family of papers, you have parameters of different nature to estimate

the (fair) price dynamics: essentially the volatility (and price movements if you have high frequency predictors)

the liquidity dynamics: that are captured (in such models) by a "baseline intensity" $A$ and an "elasticity to the fair price" one $k$. The intensity of trades filling an order being at $\delta S$ to the fair price is $A\exp -k\,\delta S$. It means that the expectation of obtaining a fill during an infinitesimal time $dt$ is $A(\exp -k\,\delta S)\, dt$.

For the an estimation of the intraday volatility they are a lot of means (see for instance How to calculate historical intraday volatility?).

For the $(A,k)$ part, it is described in Sophie's paper and at Joaquin's thesis. The principle is the following:

you want to capture the probability that an order at $\delta S$ of the fair price is filled

you look in your history and you see an order that is at a distance $\delta S_k$ at time $t_k$ and you observe when it obtained an execution (say at $t_{k+1}$)

you have your first data point: it took $\delta t_k:=t_{k+1}-t_{k}$ second to obtain a fill starting at $\delta S_k$, you collect as much as you can

then you do some data curation (as usual) because you want to focus on "stationary situations" (or a least ergodic ones): remove outliers and inconsistant data (you can even create a "environment/context" indicator and condition by it). There is a matter of "censored data" too (if this order has been cancelled).

the last step is the easiest: do the regression to obtain $(A,k)$ from your curated collection of $(\delta S_k, \delta t_k)_k$; you can do it simply using a log-linear regression, or minimize any loss function you like.

in our extension of Avellaneda - Stoikov paper, we provide some numerical examples: Dealing with the Inventory Risk. A solution to the market making problem.

in our extension of Avellaneda - Stoikov paper, we provide some numerical examples: Dealing with the Inventory Risk. A solution to the market making problem.

For this family of papers, you have parameters of different nature to estimate

the (fair) price dynamics: essentially the volatility (and price movements if you have high frequency predictors)

the liquidity dynamics: that are captured (in such models) by a "baseline intensity" $A$ and an "elasticity to the fair price" one $k$. The intensity of trades filling an order being at $\delta S$ to the fair price is $A\exp -k\,\delta S$. It means that the expectation of obtaining a fill during an infinitesimal time $dt$ is $A(\exp -k\,\delta S)\, dt$.

For the an estimation of the intraday volatility they are a lot of means (see for instance How to calculate historical intraday volatility?).

For the $(A,k)$ part, it is described in Sophie's paper and at Joaquin's thesis. The principle is the following:

you want to capture the probability that an order at $\delta S$ of the fair price is filled

you look in your history and you see an order that is at a distance $\delta S_k$ at time $t_k$ and you observe when it obtained an execution (say at $t_{k+1}$)

you have your first data point: it took $\delta t_k:=t_{k+1}-t_{k}$ second to obtain a fill starting at $\delta S_k$, you collect as much as you can

then you do some data curation (as usual) because you want to focus on "stationary situations" (or a least ergodic ones): remove outliers and inconsistant data (you can even create a "environment/context" indicator and condition by it). There is a matter of "censored data" too (if this order has been cancelled).

the last step is the easiest: do the regression to obtain $(A,k)$ from your curated collection of $(\delta S_k, \delta t_k)_k$; you can do it simply using a log-linear regression, or minimize any loss function you like.

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created Jan 11, 2022 at 17:07

in our extension of Avellaneda - Stoikov paper, we provide some numerical examples: Dealing with the Inventory Risk. A solution to the market making problem.