Abstracts

The advent of high frequency trading has changed the landscape of financial markets, leading to an environment where a variety of participants with a wide range of trading frequencies and trading constraints interact. Motivated by a detailed study of orders submitted by participants in the S&P futures market, and building on our previous work on queuing models of limit order books, we propose a stochastic model for a limit order market which attempts to capture the coexistence of different types of order flows at different time scales and explore the consequences of high frequency trading on price dynamics, volatility and liquidity. We argue that the empirical evidence points to a non-classical scaling limit for the model and show that, in this limit, the dynamics of the limit order book is governed by a stochastic PDE. The explicit form of this stochastic PDE allows in turn to study the interaction of high-frequency order flow with the rest of the market.