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Arbitrage-free interval and dynamic hedging in an illiquid market

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  • Jinqiang Yang
  • Zhaojun Yang

Abstract

This paper derives two pricing PDEs for a general European option under liquidity risk. We provide two modified hedges: one hedge replicates a short option and the other replicates a long option inclusive of liquidity costs under continuous rebalancing. We identify an arbitrage-free interval by calculating the costs of the two hedges. Unlike in a setting with infinite overall transaction costs, the overall liquidity cost in our model is proved to be finite even under continuous rebalancing. Numerical results on option pricing and the moments of hedge errors of Black--Scholes and our modified hedges are also presented.

Suggested Citation

  • Jinqiang Yang & Zhaojun Yang, 2012. "Arbitrage-free interval and dynamic hedging in an illiquid market," Quantitative Finance, Taylor & Francis Journals, vol. 13(7), pages 1029-1039, May.
  • Handle: RePEc:taf:quantf:v:13:y:2012:i:7:p:1029-1039
    DOI: 10.1080/14697688.2012.693943
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    References listed on IDEAS

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    12. Brennan, Michael J. & Schwartz, Eduardo S., 1978. "Finite Difference Methods and Jump Processes Arising in the Pricing of Contingent Claims: A Synthesis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(03), pages 461-474, September.
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