Problem bank

Problem 296 of 333EasyStochastic ProcessesP296

Where the inventory drifts

  1. A market maker trades one lot at a time. Each trade is a buy or a sell with probability 1/21/2 each, independently, so her inventory moves by +1+1 or −1-1 lot per trade, starting from flat.

    After 900 trades, what is the standard deviation of her inventory, and roughly how likely is she to be at least 60 lots long or short? How many trades does it take for the standard deviation to reach 60 lots?