Stochastic Price Dynamics Implied By the Limit Order Book

TL;DR

This paper introduces a method to infer stochastic price dynamics from the limit order book, revealing how the order book's structure implies a volatility smile and enabling the modeling of jumps in prices.

Contribution

It presents a novel approach linking limit order book data to stochastic price models, including jump-diffusion processes, to explain observed market phenomena.

Findings

Limit order book data implies a volatility smile.

A jump-diffusion process can be explicitly inferred.

The approach explains fat tails in financial data.

Abstract

In this paper we 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 when the price touches a pre-specified lower, respectively higher, limit-price. We 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. We also show how a jump-diffusion process can be explicitly inferred to account for the volatility smile.