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Discrete time hedging with liquidity risk

  • Ku, Hyejin
  • Lee, Kiseop
  • Zhu, Huaiping
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    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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    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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    1. Rüdiger Frey & Alexander Stremme, 1997. "Market Volatility and Feedback Effects from Dynamic Hedging," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 351-374.
    2. Back, Kerry, 1993. "Asymmetric Information and Options," Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 435-72.
    3. Hayne E. Leland., 1984. "Option Pricing and Replication with Transactions Costs," Research Program in Finance Working Papers 144, University of California at Berkeley.
    4. 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.
    5. 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.
    6. Umut Çetin & Robert Jarrow & Philip Protter, 2004. "Liquidity risk and arbitrage pricing theory," Finance and Stochastics, Springer, vol. 8(3), pages 311-341, 08.
    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. 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.
    9. RØdiger Frey, 1998. "Perfect option hedging for a large trader," Finance and Stochastics, Springer, vol. 2(2), pages 115-141.
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