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Using Kyle’s Lambda to Adjust Market-Maker Quotes

Article Quant Q&A · Author: Anton
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Summary

The document describes a cryptocurrency market-making question about estimating a reference price for an Avellaneda–Stoikov style inventory-control strategy. The author proposes adjusting the initial price by cumulative signed market-order volume multiplied by Kyle’s lambda, treating buy volume as positive and sell volume as negative. They report that this estimate can diverge substantially from the observed mid-price and ask what is wrong with the approach.

No answer, data analysis, or evidence is included, so the proposed calculation is not validated here. The document highlights a practical modeling issue: a cumulative order-flow adjustment can drift away from the current mid-price, and the question does not specify the estimation window, units, or calibration of lambda. It provides a problem statement rather than a resolved pricing method.

Key ideas

  • The author seeks a reference price for a cryptocurrency market-making strategy.
  • The proposed estimate adds cumulative signed market-order volume scaled by Kyle’s lambda to an initial price.
  • The resulting estimate can differ substantially from the mid-price.
  • The document asks for diagnosis but provides no solution or empirical validation.

Tags

CryptoMarket makingMarket microstructureExecution
Full text
# Kyle model for market-maker price


# Kyle model for market-maker price












Now I make research about market making for cryptocurrency. I’m using model like Avellaneda-Stoikov for optimal control inventory, and I can’t understand how to find S(t) price. Of course, taking the mid-price is not a good idea. I read a lot about Kyle’s model, and the main thing that I found, is that I need to move orders using trade volume * kyle lambda. I wrote the script on the python for finding market maker price and as you can see, sometimes a difference between mid-price and generated price is so large. My algorithm for generation: For point in time t: S(0) + (the sum of all market buy order in the range [0:t] - the sum of all market sell order in the range [0:t]) * Kyle lambda

How I can solve this? Or what I’m doing wrong?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.