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The Self-Financing Equation in High Frequency Markets

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  • Rene Carmona
  • Kevin Webster

Abstract

High Frequency Trading (HFT) represents an ever growing proportion of all financial transactions as most markets have now switched to electronic order book systems. The main goal of the paper is to propose continuous time equations which generalize the self-financing relationships of frictionless markets to electronic markets with limit order books. We use NASDAQ ITCH data to identify significant empirical features such as price impact and recovery, rough paths of inventories and vanishing bid-ask spreads. Starting from these features, we identify microscopic identities holding on the trade clock, and through a diffusion limit argument, derive continuous time equations which provide a macroscopic description of properties of the order book. These equations naturally differentiate between trading via limit and market orders. We give several applications (including hedging European options with limit orders, market maker optimal spread choice, and toxicity indexes) to illustrate their impact and how they can be used to the benefit of Low Frequency Traders (LFTs).

Suggested Citation

  • Rene Carmona & Kevin Webster, 2013. "The Self-Financing Equation in High Frequency Markets," Papers 1312.2302, arXiv.org.
    • Handle: RePEc:arx:papers:1312.2302
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    References listed on IDEAS

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    Cited by:

    1. Kyle Bechler & Mike Ludkovski, 2014. "Optimal Execution with Dynamic Order Flow Imbalance," Papers 1409.2618, arXiv.org, revised Oct 2014.
    2. Rama Cont & Marvin S. Mueller, 2019. "A stochastic partial differential equation model for limit order book dynamics," Papers 1904.03058, arXiv.org, revised May 2021.
    3. Kyle Bechler & Michael Ludkovski, 2017. "Order Flows and Limit Order Book Resiliency on the Meso-Scale," Papers 1708.02715, arXiv.org.
    4. Damiano Brigo & Federico Graceffa & Eyal Neuman, 2022. "Price impact on term structure," Quantitative Finance, Taylor & Francis Journals, vol. 22(1), pages 171-195, January.
    5. Rama Cont & Marvin Muller, 2019. "A Stochastic Pde Model For Limit Order Book Dynamics," Working Papers hal-02090449, HAL.

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