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The Journal of Derivatives

The Journal of Derivatives

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Article

Hedging Through a Limit Order Book with Varying Liquidity

Rossella Agliardi and Ramazan Gençay
The Journal of Derivatives Winter 2014, 22 (2) 32-49; DOI: https://doi.org/10.3905/jod.2014.22.2.032
Rossella Agliardi
is an associate professor in the Department of Mathematics at the University of Bologna and IMATI- CNR in Pavia, Italy. rossella.agliardi@unibo.it
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Ramazan Gençay
is a professor in the Department of Economics at Simon Fraser University in Burnaby, British Columbia, Canada, and a senior fellow at the Rimini Center for Economic Analysis in Rimini, Italy. rgencay@sfu.ca
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Abstract

Market impact is one of the most important aspects of real-world trading. It is typically a major component of transaction costs, and trading strategies are carefully optimized to minimize it. But most of the research has focused on one-off trades, not the repeated series of transactions required in delta-hedging an options position. In this article, the authors explore optimal hedging in an illiquid environment for a large trader whose trades absorb a nonmarginal fraction of the standing orders in the limit order book. The trader needs to take account of both the immediate price impact of each trade and the speed at which the limit order book is restored afterward—the market’s resilience. These two aspects of market dynamics together can produce a permanent effect of a big trade and also a temporary one that dissipates over time. Depending on the parameters of the liquidity process, the optimal strategy can be the canonical Black–Scholes delta hedge (in the limiting case of infinite liquidity) or one that is distinctly less volatile (when market impact is large, but there is some resilience in prices) or even one that entails price manipulation (when there is no resilience and the price impact is permanent).

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The Journal of Derivatives: 22 (2)
The Journal of Derivatives
Vol. 22, Issue 2
Winter 2014
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Hedging Through a Limit Order Book with Varying Liquidity
Rossella Agliardi, Ramazan Gençay
The Journal of Derivatives Nov 2014, 22 (2) 32-49; DOI: 10.3905/jod.2014.22.2.032

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Hedging Through a Limit Order Book with Varying Liquidity
Rossella Agliardi, Ramazan Gençay
The Journal of Derivatives Nov 2014, 22 (2) 32-49; DOI: 10.3905/jod.2014.22.2.032
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  • Article
    • Abstract
    • THE SETUP
    • HEDGING UNDER A PERFECTLY RESILIENT MARKET
    • HEDGING WITH PRICE IMPACT AND RESILIENCE
    • FURTHER REMARKS AND POSSIBLE EXTENSIONS
    • CONCLUSIONS
    • APPENDIX
    • ENDNOTES
    • REFERENCES
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More in this TOC Section

  • An Alternative Option to Portfolio Rebalancing
  • Editor’s Letter
  • The Second Partial Derivative of Option Price with Respect to the Strike: A Historical Reminiscence
Show more Article

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