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Discrete time hedging with liquidity risk

Author

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  • Ku, Hyejin
  • Lee, Kiseop
  • Zhu, Huaiping

Abstract

We study a discrete time hedging and pricing problem in a market with liquidity costs. Using Leland’s discrete time replication scheme [Leland, H.E., 1985. Journal of Finance, 1283–1301], we consider a discrete time version of the Black–Scholes model and a delta hedging strategy. We derive a partial differential equation for the option price in the presence of liquidity costs and develop a modified option hedging strategy which depends on the size of the parameter for liquidity risk. We also discuss an analytic method of solving the pricing equation using a series solution.

Suggested Citation

  • Ku, Hyejin & Lee, Kiseop & Zhu, Huaiping, 2012. "Discrete time hedging with liquidity risk," Finance Research Letters, Elsevier, vol. 9(3), pages 135-143.
  • Handle: RePEc:eee:finlet:v:9:y:2012:i:3:p:135-143
    DOI: 10.1016/j.frl.2012.02.002
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    References listed on IDEAS

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    1. Peter Bank & Dietmar Baum, 2004. "Hedging and Portfolio Optimization in Financial Markets with a Large Trader," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 1-18.
    2. 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..
    3. Leland, Hayne E, 1985. " Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
    4. U. Çetin & R. Jarrow & P. Protter & M. Warachka, 2008. "Pricing Options in an Extended Black Scholes Economy with Illiquidity: Theory and Empirical Evidence," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 9, pages 185-221 World Scientific Publishing Co. Pte. Ltd..
    5. Ajay Subramanian & Robert A. Jarrow, 2001. "The Liquidity Discount," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 447-474.
    6. Rüdiger Frey & Alexander Stremme, 1997. "Market Volatility and Feedback Effects from Dynamic Hedging," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 351-374.
    7. RØdiger Frey, 1998. "Perfect option hedging for a large trader," Finance and Stochastics, Springer, vol. 2(2), pages 115-141.
    8. Back, Kerry, 1993. "Asymmetric Information and Options," Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 435-472.
    9. 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..
    10. Robert A. Jarrow, 2008. "Derivative Security Markets, Market Manipulation, and Option Pricing Theory," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 7, pages 131-151 World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. repec:taf:oaefxx:v:5:y:2017:i:1:p:1364902 is not listed on IDEAS
    2. Chen, Son-Nan & Chiang, Mi-Hsiu & Hsu, Pao-Peng & Li, Chang-Yi, 2014. "Valuation of quanto options in a Markovian regime-switching market: A Markov-modulated Gaussian HJM model," Finance Research Letters, Elsevier, vol. 11(2), pages 161-172.

    More about this item

    Keywords

    Discrete time; Liquidity cost; Delta hedging;

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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