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Stochastic Price Dynamics Implied By the Limit Order Book

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  • Alex Langnau
  • Yanko Punchev

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.

Suggested Citation

  • Alex Langnau & Yanko Punchev, 2011. "Stochastic Price Dynamics Implied By the Limit Order Book," Papers 1105.4789, arXiv.org.
  • Handle: RePEc:arx:papers:1105.4789
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    File URL: http://arxiv.org/pdf/1105.4789
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    References listed on IDEAS

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    1. B. Tóth & J. Kertész & J. D. Farmer, 2009. "Studies of the limit order book around large price changes," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 71(4), pages 499-510, October.
    2. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Science & Finance (CFM) working paper archive 0203511, Science & Finance, Capital Fund Management.
    3. Roberto Pascual & David Veredas, 2009. "What pieces of limit order book information matter in explaining order choice by patient and impatient traders?," Quantitative Finance, Taylor & Francis Journals, vol. 9(5), pages 527-545.
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    Cited by:

    1. Kovaleva, P. & Iori, G., 2012. "Optimal Trading Strategies in a Limit Order Market with Imperfect Liquidity," Working Papers 12/05, Department of Economics, City University London.

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