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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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    7. Rama Cont & Arseniy Kukanov & Sasha Stoikov, 2010. "The Price Impact of Order Book Events," Working Papers hal-00545745, HAL.
    8. 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.
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    13. Zoltan Eisler & Janos Kertesz & Fabrizio Lillo, 2007. "The limit order book on different time scales," Papers 0705.4023, arXiv.org.
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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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