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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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