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Perfect option hedging for a large trader

RØdiger Frey ()
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RØdiger Frey: Department of Mathematics, ETH ZØrich, ETH-Zentrum, CH-8092 ZØrich, Switzerland

Finance and Stochastics, 1998, vol. 2, issue 2, 115-141

Abstract: Standard derivative pricing theory is based on the assumption of agents acting as price takers on the market for the underlying asset. We relax this hypothesis and study if and how a large agent whose trades move prices can replicate the payoff of a derivative security. Our analysis extends prior work of Jarrow to economies with continuous security trading. We characterize the solution to the hedge problem in terms of a nonlinear partial differential equation and provide results on existence and uniqueness of this equation. Simulations are used to compare the hedging strategies in our model to standard Black-Scholes strategies.

Keywords: Option pricing; Black-Scholes model; hedging; large trader; feedback effects (search for similar items in EconPapers)
JEL-codes: G12 G13 (search for similar items in EconPapers)
Date: 1998-02-12
Note: received: April 1996; final version received: April 1997
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