Estimating Order-Arrival Parameters for Avellaneda–Stoikov Market Making
Summary
The document explains how to estimate inputs for an optimal bid–ask spread model, using a stock as an example. It distinguishes price-process inputs such as drift and volatility from order-arrival inputs, and notes that the cited model does not include a tick-size parameter; quotes must ultimately be rounded to valid price increments.
For order arrivals, the response describes estimating market-order frequency from traded volume and average order size, using a power-law distribution for order sizes, and estimating temporary price impact from historical data or prior research. Combining these ingredients yields an exponential relationship between quote distance and arrival intensity, with its parameters derived from the estimated frequency, order-size distribution, and impact scale. The answer offers a parameter-estimation outline rather than a worked stock example, so it does not supply calibrated values or address practical data choices in detail.
Key ideas
- Estimate drift and volatility from the stock’s price data using a suitable statistical method.
- The cited model has no explicit tick-size input, so quotes need to be rounded to valid price increments.
- Estimate market-order frequency from traded volume and average market-order size.
- Order-size behavior and temporary price impact inform the parameters of the exponential fill-intensity function.
- The response gives an estimation framework but no calibrated example for the stock in the question.
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Full text
# Finding parameters of an utility function in a market making strategy to apply it in practice
# Finding parameters of an utility function in a market making strategy to apply it in practice
I am reading this paper below about optimal bid-ask spread in a market making strategy. It finds an approximation for optimal solution, but I cannot understand how it's practice to set the parameters for a sample stock (eg. AAPL). Assuming, I have this stock below, how I can find all the parameters for the optimal bid-ask spread?
-> How to set $A$ and $k$, for my example stock? Which is the parameter for the tick size?
Example:
Stock: AAPL
$\sigma = 0.2$
$\mu = 0.01$
$S_t$= 169.23 USD
Tick=0.01 USD
Utility function to maxime
Intensity function
How fast my order (bid/ask) will be filled respect to the mid-price in the market at t
Optimal bid/ask quote (final solution)
page 13
Paper source: Dealing with the Inventory Risk. A solution to the market making problem https://arxiv.org/abs/1105.3115
## Answer by ragoragino (score 3)
https://quant.stackexchange.com/a/37561
All the parameters of the solution need to be estimated for your specific stock. Stochastic process-specific parameters, i.e. $\mu$, $\sigma$, have to be estimated by some classical method (e.g. MLE, minimum contrast, etc.). No parameter of tick size is incorporated in the model, you will have to decide at the end whether the in-between quote shall be assigned to the higher or lower price value. And parameters relating to the order arrival need to be estimated similarly as derived in the original paper of Avellaneda & Stoikov. There you may find the derivation from three separate formulas:
- Constant frequency $\Lambda$ of market buy/sell orders estimated by dividing the total volume traded over a day by the average size of market orders on that day.
- The distribution parameter of the size of market orders $$ f^{Q}(x) \propto x^{-1-\alpha} $$
where $\alpha$ will be overtaken from the literature (presented in the original study), or else needs to be calculated from your specific dataset.
- Temporary impact of a large market order:
$$ \Delta p \propto ln(Q), $$
also either overtaken from the literature or estimated on the historical values of your specific stock.
By putting all these three formulas together, you obtain the original result:
$$ \lambda(\delta) = Aexp(-k\delta), $$
where $A = \Lambda / \alpha$ and $k = \alpha K$, $K$ being a scaling parameter for the temporary impact of a market order.
Source: Avellaneda, Marco, and Sasha Stoikov. "High-frequency trading in a limit order book." Quantitative Finance 8.3 (2008): pp. 220. https://www.math.nyu.edu/faculty/avellane/HighFrequencyTrading.pdfShown 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.