Stochastic Price Dynamics Implied By The Limit Order Book
In this paper, the authors present a novel approach to the determination of fat tails in financial data by studying the information contained in the limit order book. In an order-driven market buyers and sellers may submit limit orders, which are executed if the price touches a pre-specified lower, respectively higher, limit-price. They show that, in equilibrium, the collection of all such orders - the limit order book - implies a volatility smile, similar to observations from option pricing in the Black-Scholes model. They also show how a jump-diffusion process can be explicitly inferred to account for the volatility smile.