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Mean-Variance Hedging with Uncertain Trade Execution

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  • Koichi Matsumoto

Abstract

This paper studies a hedging problem of a contingent claim in a discrete time model. The contingent claim is hedged by one illiquid risky asset and the hedging error is measured by a quadratic criterion. In our model, trade does not always succeed and then trade times are not only discrete, but also random. The uncertainty of trade execution represents the liquidity risk. First we find an optimal hedging strategy with fixed initial condition. Next we consider an optimal initial condition. Finally, we study a binomial model as a simple example.

Suggested Citation

  • Koichi Matsumoto, 2009. "Mean-Variance Hedging with Uncertain Trade Execution," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(3), pages 219-252.
  • Handle: RePEc:taf:apmtfi:v:16:y:2009:i:3:p:219-252
    DOI: 10.1080/13504860802583972
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    References listed on IDEAS

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    1. Martin Schweizer, 1995. "Variance-Optimal Hedging in Discrete Time," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 1-32, February.
    2. Koichi Matsumoto, 2006. "Optimal portfolio of low liquid assets with a log-utility function," Finance and Stochastics, Springer, vol. 10(1), pages 121-145, January.
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    4. Robert A. Jarrow, 2008. "Market Manipulation, Bubbles, Corners, and Short Squeezes," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 6, pages 105-130, World Scientific Publishing Co. Pte. Ltd..
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    7. Umut Çetin & Robert A. Jarrow & Philip Protter, 2008. "Liquidity risk and arbitrage pricing theory," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 8, pages 153-183, World Scientific Publishing Co. Pte. Ltd..
    8. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
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    10. Ajay Subramanian & Robert A. Jarrow, 2001. "The Liquidity Discount," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 447-474, October.
    11. Huyên Pham, 2000. "On quadratic hedging in continuous time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(2), pages 315-339, April.
    12. Takuji Arai, 2005. "An extension of mean-variance hedging to the discontinuous case," Finance and Stochastics, Springer, vol. 9(1), pages 129-139, January.
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    Cited by:

    1. Koichi Matsumoto & Keita Shimizu, 2020. "Hedging Derivatives on Two Assets with Model Risk," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 27(1), pages 83-95, March.
    2. Rossella Agliardi & Ramazan Gençay, 2012. "Hedging through a Limit Order Book with Varying Liquidity," Working Paper series 12_12, Rimini Centre for Economic Analysis.

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