Title: The Pricing and Hedging of Options in Finitely Elastic Markets
Abstract: Standard derivative pricing theory is based on the assumption of the market for the underlying asset being infinitely elastic. We relax this hypothesis and study if and how a large agent whose trades move prices can replicate the payoff of a derivative contract. Our analysis extends a prior work of Jarrow who has analyzed this question in a binomial setting 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 hedge ratio in our model to standard Black-Scholes strategies. Moreover, we discuss how standard option pricing theory can be extended to finitely elastic markets.
Keywords: market microstructure, feedback effects
Creation-Date: June 1996
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