Calibrating Market-Making Intensity in Illiquid, Volatile Markets

Summary

The document describes a calibration problem in the Guéant–Lehalle–Fernandez-Tapia market-making model. The author estimates bid- and ask-side order-arrival intensities using the last traded price as a reference, updating it at short intervals, and separates trades by aggressor side in an attempt to improve the fit. These choices did not resolve the difficulty: the model's exponential intensity function produces poor estimates of its parameters in an illiquid, highly volatile market.

The author asks whether another functional form or different calibration practices would be more suitable. No alternative model, empirical comparison, or fitted results are provided, so the document identifies a practical limitation rather than establishing a solution. Its main research implication is that intensity estimates may depend on market conditions, reference-price construction, sampling intervals, and trade classification; these choices should be examined when applying a standard market-making model outside liquid, stable settings.

Key ideas

• The document applies the Guéant–Lehalle–Fernandez-Tapia model to estimate bid- and ask-side trading intensities.
• It uses the last traded price as a reference and updates it at short intervals.
• Separating trades by aggressor side did not improve the exponential intensity fit in the described setting.
• The author raises alternative intensity functions and calibration practices as open questions for illiquid, volatile markets.

Tags

# Issues with Calibrating Intensity Functions in Illiquid and High-Volatility Markets for Market Making


# Issues with Calibrating Intensity Functions in Illiquid and High-Volatility Markets for Market Making












I am calibrating intensity functions for bid and ask spreads using the Guéant–Lehalle–Fernandez-Tapia model from Olivier Guéant's "Optimal Market Making" paper. However, I'm facing issues with the parameters 𝐴 and 𝑘 due to the market being illiquid and highly volatile.

I used last traded price as reference price and update it every small period of time (10 seconds to 1 minute). The figure shows 15 seconds interval. I decided to split trades for better accuracy (didn't help) according to who was trade initiator (who posted limit order).

But the exponential intensity function seems inappropriate, leading to poor calibration of 𝐴 and 𝑘.

Are there alternative functional forms for intensity functions suitable for illiquid and volatile markets? What are best practices for calibrating intensity functions in these conditions?

Any insights would be appreciated.

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