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A String Model of Liquidity in Financial Markets

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  • Sergey Lototsky
  • Henry Schellhorn
  • Ran Zhao

Abstract

We consider a dynamic market model of liquidity where unmatched buy and sell limit orders are stored in order books. The resulting net demand surface constitutes the sole input to the model. We prove that generically there is no arbitrage in the model when the driving noise is a stochastic string. Under the equivalent martingale measure, the clearing price is a martingale, and options can be priced under the no-arbitrage hypothesis. We consider several parameterized versions of the model, and show some advantages of specifying the demand curve as quantity as a function of price (as opposed to price as a function of quantity). We calibrate our model to real order book data, compute option prices by Monte Carlo simulation, and compare the results to observed data.

Suggested Citation

  • Sergey Lototsky & Henry Schellhorn & Ran Zhao, 2016. "A String Model of Liquidity in Financial Markets," Papers 1608.05900, arXiv.org, revised Apr 2018.
    • Handle: RePEc:arx:papers:1608.05900
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    References listed on IDEAS

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