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Discrete time hedging with liquidity risk

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

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    File URL: http://www.sciencedirect.com/science/article/pii/S1544612312000141
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    Bibliographic Info

    Article provided by Elsevier in its journal Finance Research Letters.

    Volume (Year): 9 (2012)
    Issue (Month): 3 ()
    Pages: 135-143

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    Handle: RePEc:eee:finlet:v:9:y:2012:i:3:p:135-143

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    Web page: http://www.elsevier.com/locate/frl

    Related research

    Keywords: Discrete time; Liquidity cost; Delta hedging;

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    References

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    1. Leland, Hayne E, 1985. " Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
    2. RØdiger Frey, 1998. "Perfect option hedging for a large trader," Finance and Stochastics, Springer, vol. 2(2), pages 115-141.
    3. Rüdiger Frey & Alexander Stremme, 1997. "Market Volatility and Feedback Effects from Dynamic Hedging," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 351-374.
    4. Jarrow, Robert A., 1992. "Market Manipulation, Bubbles, Corners, and Short Squeezes," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(03), pages 311-336, September.
    5. Umut Çetin & Robert Jarrow & Philip Protter, 2004. "Liquidity risk and arbitrage pricing theory," Finance and Stochastics, Springer, vol. 8(3), pages 311-341, 08.
    6. Jarrow, Robert A., 1994. "Derivative Security Markets, Market Manipulation, and Option Pricing Theory," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(02), pages 241-261, June.
    7. U. �etin & R. Jarrow & P. Protter & M. Warachka, 2006. "Pricing Options in an Extended Black Scholes Economy with Illiquidity: Theory and Empirical Evidence," Review of Financial Studies, Society for Financial Studies, vol. 19(2), pages 493-529.
    8. Back, Kerry, 1993. "Asymmetric Information and Options," Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 435-72.
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