Discrete time hedging with liquidity risk |
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| Authors: | Hyejin Ku Kiseop Lee Huaiping Zhu |
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| Affiliation: | 1. Department of Obstetrics and Gynecology, Olive View-UCLA Medical Center, 14445 Olive View Dr., Sylmar, CA 91342, United States;2. Department of Obstetrics and Gynecology, David Geffen School of Medicine at UCLA, 10833 Le Conte Avenue, Room 951740, Los Angeles, CA 90095, United States;3. Department of Medicine Statistics Core, David Geffen School of Medicine at UCLA, 911 Broxton Ave., Los Angeles, CA 90024, United States;1. School of Arts and Science, Suqian College, Suqian, Jiangsu, 223800, PR China;2. Laboratory of Mathematical Parallel Systems (Lamps), Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada;3. Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi, 030006, PR China;1. Department of Radiation Oncology and Molecular Radiation Sciences, Johns Hopkins University School of Medicine, Baltimore, MD, United States;2. Department of Gynecology and Obstectrics, Johns Hopkins University School of Medicine, Baltimore, MD, United States |
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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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