A Stochastic Model for Order Book Dynamics in Online Product Markets

We introduce a stochastic model for order book dynamics in online product markets, where product prices basically follow a random walk, but sometimes exhibit a sharp decline like cascade. In this model, each e-retailer stochastically places a limit sell order, stochastically reviews its quote price, and revise the quote price if necessary. On the other hand, customers stochastically pick a particular e-retailer and purchase its product. We conduct a numerical simulation to show that the model succesfully reproduces some important facts regarding price dynamics in online product markets, including a Hurst exponent around 0.5, non-autocorrelation of price fluctuations, non-trivial complex correlation of the sign of price changes, and the fat tails of price change distributions.