We investigate the stationary state of some Poisson limit order book models. We derive explicit formulas for the shape of the order book when the sizes of submitted orders can vary. Results provide useful insights that are empirically verified. We also derive formulas for the distribution of the liquidity offered at the best quote, highlighting the importance of aggressive limit and market orders in order book modeling.
Back to Workshop II: The Mathematics of High Frequency Financial Markets: Limit Order Books, Frictions, Optimal Execution and Program Trading