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Hard · Market Microstructure · Quant Trader interview question · market-microstructure, queue-position, poisson-process, expected-value, probability
You are a market maker who places a limit buy order for 100 shares at the best bid. You are currently 10th in the queue at that price level (i.e., there are 9 orders ahead of you). Market sell orders arrive and execute against the orders at this price level according to a Poisson process with rate $ \lambda = 5 $ orders per second. Simultaneously, traders ahead of you in the queue may cancel their orders. Cancellations from each trader ahead of you occur according to an independent Poisson proce