calibrate the lambda

[TIANRENK]

I followed the example in the document caculated the lambda of Guéant–Lehalle–Fernandez-Tapia Market Making Model. I found the market order’s arrivals does not match the Poisson distribution. How can I better calibrate the lambda .

[TIANRENK]

I followed the example in the document caculated the lambda of Guéant–Lehalle–Fernandez-Tapia Market Making Model. I found the market order’s arrivals match the Poisson distribution. How can I better calibrate the lambda .

The market order's hits just 0.5 ticksize over 85%.

[nkaz001]

I've also noticed the same phenomenon, but I lack a definite answer. As you pointed out, a non-parametric approach seems necessary. One straightforward method that occurs to me involves using the median or decile to directly measure order arrival, leading to an empirical derivation of half spread and skew. For instance, half_spread could be calculated as a * decile(order_arrival, d) + b, with skew described similarly. Starting with an identity function(a = 1 and b = 0) would offer the simplest initial approach.